inequality word problem homework

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Writing Inequalities from Word Problems

Learn about writing inequalities from word problems with help from our practice examples. If you want to test yourself, or get some practice, then try one of our graded worksheets, or our online quiz.

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What is an Inequality?

The language of inequalities.

• How to Write an Inequality from a Word Problem
• Write an Inequality from a Word Problems Examples

Writing Inequalities from Word Problems Worksheets

• Writing Inequalities from Word Problems Online Quiz
• More related resources

An inequality is when you have a relationship between two values of expressions which are not equal to each other.

There are a few different options for different types of inequalities:

• Greater than (>) where one expression or value is greater than another, e.g. 7 > 5
• Less than (<) where one expression or value is less than another, e.g. 9 < 2 x 6
• Greater than or equal to (≥) where one expression or value is greater than or equal to another, e.g. 20 + 4 ≥ 17
• Less than or equal to (≤) where one expression or value is less than or equal to another, e.g. 18 ≤ 9 x 2
• Not equal to (≠) where one expression or value is not equal to another, e.g. 7 ≠ 4

When writing inequalities from word problems, we have to look carefully at and understand the language being used.

Different words and phrases have different meanings when deciding on which inequality to use.

The mathematical notation is really just a shorthand way of writing the words more efficiently and clearly.

Here is a quick table showing some of the written expressions often used and which inequality they are represented by.

Note: the word 'between' is mainly used to mean between inclusively (including end points).

However, sometimes 'between' is used to mean between exclusively (excluding end points).

To avoid ambiguity, it is good practice to include the word 'inclusive' or 'exclusive' to make it completely clear if the end points are included or not.

Some simple examples showing inequalities from phrases:

The variable names (letters) have been chosen at random - you can use any variable name to represent any value.

Note: you need to read the word problem carefully because sometimes the inequality does not match the language used, especially when the inequality involves finding out what is left over or what remains after an amount is taken away. See Examples 2) and 7) below.

How to Write Inequalities from Word Problems

When we are writing an inequality from a word problem, we are basically translating the word problem into mathematical language and symbols.

When writing an inequality from a word problem, there are two simple steps you need to follow...

Step 1) Read the word problem carefully and change the word problem into algebra.

• use the language of inequalities table to help you select the right inequality

Step 2) Use algebra to solve the word problem

Step 3) rewrite the inequality using algebra., write an inequality from a word problem examples.

The best way to learn how to write inequalities from word problems and see how they work is to look at some ready made examples.

Writing Inequalities from Word Problems - Basic Examples

Here are some examples of writing inequalities from word problems.

Example 1) Sally bakes some cookies and needs to put them in the over for at least 12 minutes. Write an inequality using the variable t to show how long the cookies need to be baked in the oven.

The vocabulary which tells us about the inequality are the words: at least .

This means we need to use the ≥ symbol.

So the inequality is t ≥ 12 minutes

Example 2) Newton has a 30 ounce bottle of water. He drinks over half of the bottle. Write an inequality using the variable c to show how many ounces are left in the bottle.

The vocabulary which tells us about the inequality are the words: over .

However, because he has drunk over half the bottle, it means that there is under half a bottle left.

So the symbol we need is < and the amount is ½ of 30 = 15.

So the inequality is b < 15 ounces

Example 3) Anna is more than three times as old as Bertie. If Bertie is 8 years old, write an inequality using the variable A to show how old Anna is.

The vocabulary which tells us about the inequality are the words: more than .

So the symbol we need is > and the amount is 3 x 8 = 24.

So the inequality is A > 24 years old

Example 4) A book has 14 chapters.The shortest chapter has 12 pages. Write an inequality using the variable p to show how many pages the book has.

The vocabulary which tells us about the inequality are the words: shortest .

If the shortest chapter has 11 pages, then there must be some chapters with more than 11 pages.

So the symbol we need is > and the amount is 14 x 12 = 168.

So the inequality is p > 168 pages.

Writing Inequalities from Word Problems -Intermediate Examples

These examples use two different variables and express one variable in terms of another.

Example 5) Captain and Frazer have some gold coins. Captain has at least three times as many coins as Frazer. Write an inequality for the number of coins Captain has (c) in terms of the number of coins Frazer has (f).

So the symbol we need is ≥

So the inequality is c ≥ 3f.

Example 6) In a hotel there are f flights of stairs. Each flight has a maximum of 12 steps. There are also 3 steps up to the main entrance. Write an expression for the total number of steps, s, in terms of f.

The vocabulary which tells us about the inequality are the words: a maximum of .

So the symbol we need is ≤

We know that there are f flights of steps and also 3 extra steps.

So the inequality is s ≤ 12f + 3.

Writing Inequalities from Word Problems - Harder Examples

These examples involve solving word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers.

There are also examples where the variable lies between two values.

Example 7) Captain has a one-liter bottle of water. He drinks more than one-quarter of the bottle but less than one-half of the bottle. Write an inequality using the variable b to show the amount of water than is left in the bottle.

The vocabulary which tells us about the inequality are the words: more than and less than .

However, because we are looking at what is left in the bottle, rather than what has been drunk, we need to think carefully about the inequalities!

He drinks more than one-quarter of the bottle, so there will be less than three-quarters of the bottle left, so we need the symbol <

He drinks less than one-half of the bottle, so there will be one-half or more of the bottle left, so we need the symbol ≥

Half of the bottle = ½ liters = 500 ml. 1000 - 500 = 500 ml

Quarter of the bottle = ¼ liters = 250 ml. 1000 - 250 = 750 ml

So the inequality is b ≥ 500 ml and b < 750 ml This can be simplified to: 500 ≤ b < 750 ml This means that he has at least 500 ml but less than 750 ml left.

Example 8) Captain has challenged himself to catch a minimum of 50 fish from a lake. He manages to catch 8 of them and put them in his bucket. If he catches 6 fish every hour, write an inequality to show the time (t) in hours it will take him to reach his target.

The vocabulary which tells us about the inequality are the words: a minimum of .

The inequality we get from this problem is 6t + 8 ≥ 50

We are not finished yet, because this needs to be simplified and written in terms of t.

6t + 8 ≥ 50 so 6t ≥ 42

If we divide both sides of this inequality by 6, we get:

So the inequality is t ≥ 7 hours He needs to fish for at least 7 hours to reach his target.

Example 9) It takes Newton between 23 and 28 seconds (inclusive) to swim a length of a swimming pool. Write an inequality using the variable t to show how long it will take him to swim 3 lengths.

The vocabulary which tells us about the inequality are the words: between (inclusive) .

So the symbol we need is ≤ and ≥

3 x 23 = 69 and 3 x 28 = 84

So the inequality is t ≥ 69 and t ≤ 84 This can be simplified to: 69 ≤ t ≤ 84 It will take him between 69 and 84 seconds (inclusive) to swim 3 lengths.

We have a range of different inequality worksheets which involve writing inequalities from a range of word problems..

We have split the sheets into 3 sections: A, B and C

• Section A involves basic level questions aimed at 6th grade
• Section B involves medium level questions aimed at 6th and 7th grade
• Section C involves more advanced questions aimed at 7th and 8th grade

Writing Inequalities from Word Problems - Section A Easier

Sheet 1 involves picking the vocabulary and relevant information from the problem and writing the inequality

Sheet 2 involves the same skills as Sheet 1, but also involves an arithmetic operation to get the inequality.

• Inequalities from Word Problems Sheet A1
• PDF version
• Inequalities from Word Problems Sheet A2

Writing Inequalities from Word Problems - Section B Medium

Sheet 1 involves using two variables and writing an inequality for one variable in terms of the other variable

Sheet 2 is similar to Sheet 1 but with slightly harder problems.

• Inequalities from Word Problems Sheet B1
• Inequalities from Word Problems Sheet B2

Writing Inequalities from Word Problems - Section C

Sheet 1 involves using one variables and using the information to solve the inequality, usually in the form px + q > r or px + q < r, where p, q, and r are specific rational numbers

Sheet 2 involves the same skills as Sheet 1 but has compound inequalities in each question

• Inequalities from Word Problems Sheet C1
• Inequalities from Word Problems Sheet C2

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6th Grade Ratio and Unit Rate Worksheets

These 5th grade ratio worksheets are a great way to introduce this concept.

We have a range of part to part ratio worksheets and slightly harder problem solving worksheets.

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6th Grade Algebra Worksheets

If you are looking for some 6th grade algebra worksheets to use with your child to help them understand simple equations then try our selection of basic algebra worksheets.

There are a range of 6th grade math worksheets covering the following concepts:

• Generate the algebra - and write your own algebraic expressions;
• Calculate the algebra - work out the value of different expressions;
• Solve the algebra - find the value of the term in the equation.
• Use the distributive property to factorize and expand different expressions
• 6th Grade Distributive Property Worksheets
• Expressions and Equations 6th Grade
• Basic Algebra Worksheets (6th & 7th Grade)

Writing Inequalities from Word Problems Quiz

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This quick quiz tests your skill at writing inequalities from a range of word problems.

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Inequalities Word Problems Worksheets

Inequalities word problems worksheets can help encourage students to read and think about the questions, rather than simply recognizing a pattern to the solutions.Inequalities word problems worksheet come with the answer key and detailed solutions which the students can refer to anytime.

Benefits of Inequalities Word Problems Worksheets

Inequalities word problems worksheets help kids to improve their speed, accuracy, logical and reasoning skills.

Inequalities word problems worksheets gives students the opportunity to solve a wide variety of problems helping them to build a robust mathematical foundation. Inequalities word problems worksheets helps kids to improve their speed, accuracy, logical and reasoning skills in performing simple calculations related to the topic of inequalities.

Inequalities word problems worksheets are also helpful for students to prepare for various competitive exams.

These worksheets come with visual simulation for students to see the problems in action, and provides a detailed step-by-step solution for students to understand the process better, and a worksheet properly explained about the Inequalities.

Download Inequalities Word Problems Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

☛ Check Grade wise Inequalities Word Problems Worksheets

• 7th Grade Inequalities Worksheets

Solving Inequality Word Questions

(You might like to read Introduction to Inequalities and Solving Inequalities first.)

In Algebra we have "inequality" questions like:

Sam and Alex play in the same soccer team. Last Saturday Alex scored 3 more goals than Sam, but together they scored less than 9 goals. What are the possible number of goals Alex scored?

How do we solve them?

The trick is to break the solution into two parts:

Turn the English into Algebra.

Then use Algebra to solve.

Turning English into Algebra

To turn the English into Algebra it helps to:

• Read the whole thing first
• Do a sketch if needed
• Assign letters for the values
• Find or work out formulas

We should also write down what is actually being asked for , so we know where we are going and when we have arrived!

The best way to learn this is by example, so let's try our first example:

Assign Letters:

• the number of goals Alex scored: A
• the number of goals Sam scored: S

We know that Alex scored 3 more goals than Sam did, so: A = S + 3

And we know that together they scored less than 9 goals: S + A < 9

We are being asked for how many goals Alex might have scored: A

Sam scored less than 3 goals, which means that Sam could have scored 0, 1 or 2 goals.

Alex scored 3 more goals than Sam did, so Alex could have scored 3, 4, or 5 goals .

• When S = 0, then A = 3 and S + A = 3, and 3 < 9 is correct
• When S = 1, then A = 4 and S + A = 5, and 5 < 9 is correct
• When S = 2, then A = 5 and S + A = 7, and 7 < 9 is correct
• (But when S = 3, then A = 6 and S + A = 9, and 9 < 9 is incorrect)

Lots More Examples!

Example: Of 8 pups, there are more girls than boys. How many girl pups could there be?

• the number of girls: g
• the number of boys: b

We know that there are 8 pups, so: g + b = 8, which can be rearranged to

We also know there are more girls than boys, so:

We are being asked for the number of girl pups: g

So there could be 5, 6, 7 or 8 girl pups.

Could there be 8 girl pups? Then there would be no boys at all, and the question isn't clear on that point (sometimes questions are like that).

• When g = 8, then b = 0 and g > b is correct (but is b = 0 allowed?)
• When g = 7, then b = 1 and g > b is correct
• When g = 6, then b = 2 and g > b is correct
• When g = 5, then b = 3 and g > b is correct
• (But if g = 4, then b = 4 and g > b is incorrect)

A speedy example:

Example: Joe enters a race where he has to cycle and run. He cycles a distance of 25 km, and then runs for 20 km. His average running speed is half of his average cycling speed. Joe completes the race in less than 2½ hours, what can we say about his average speeds?

• Average running speed: s
• So average cycling speed: 2s
• Speed = Distance Time
• Which can be rearranged to: Time = Distance Speed

We are being asked for his average speeds: s and 2s

The race is divided into two parts:

• Distance = 25 km
• Average speed = 2s km/h
• So Time = Distance Average Speed = 25 2s hours
• Distance = 20 km
• Average speed = s km/h
• So Time = Distance Average Speed = 20 s hours

Joe completes the race in less than 2½ hours

• The total time < 2½
• 25 2s + 20 s < 2½

So his average speed running is greater than 13 km/h and his average speed cycling is greater than 26 km/h

In this example we get to use two inequalities at once:

Example: The velocity v m/s of a ball thrown directly up in the air is given by v = 20 − 10t , where t is the time in seconds. At what times will the velocity be between 10 m/s and 15 m/s?

• velocity in m/s: v
• the time in seconds: t
• v = 20 − 10t

We are being asked for the time t when v is between 5 and 15 m/s:

So the velocity is between 10 m/s and 15 m/s between 0.5 and 1 second after.

And a reasonably hard example to finish with:

Example: A rectangular room fits at least 7 tables that each have 1 square meter of surface area. The perimeter of the room is 16 m. What could the width and length of the room be?

Make a sketch: we don't know the size of the tables, only their area, they may fit perfectly or not!

• the length of the room: L
• the width of the room: W

The formula for the perimeter is 2(W + L) , and we know it is 16 m

• 2(W + L) = 16
• L = 8 − W

We also know the area of a rectangle is the width times the length: Area = W × L

And the area must be greater than or equal to 7:

• W × L ≥ 7

We are being asked for the possible values of W and L

Let's solve:

So the width must be between 1 m and 7 m (inclusive) and the length is 8−width .

• Say W = 1, then L = 8−1 = 7, and A = 1 x 7 = 7 m 2 (fits exactly 7 tables)
• Say W = 0.9 (less than 1), then L = 7.1, and A = 0.9 x 7.1 = 6.39 m 2 (7 won't fit)
• Say W = 1.1 (just above 1), then L = 6.9, and A = 1.1 x 6.9 = 7.59 m 2 (7 fit easily)
• Likewise for W around 7 m

Lesson Solving word problems on inequalities

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Inequality Word Problems Worksheets

We use inequalities to compare two values. They give us an idea of relative size by stating that one is greater, lesser, equal, or not equal to the other value. Many times, when we use math, we do not need an exact answer, just an idea if something is going to work. I was reminded of this concept this very morning. I am a lacrosse coach and I have a bag that carries 80 lacrosse balls. There were already 28 balls in the bag and the school bought me a 50 pack of new balls. I had to quickly understand if that entire pack would fit in my bag. With the help of a quick inequality, I figured out there were too many for the bag. These worksheets and lessons help students learn how to write inequalities when given a word problem.

Aligned Standard: Grade 7 Expression & Equations - 7.EE.B.4b

• Amanda and Her Flowers Step-by-step Lesson - How many lilies can she afford? She wants to buy a pair of red rose flowers for $18 and spend the rest on lily flowers. Each lily flower costs $11. Write an inequality for the number of lily flowers she can purchase.
• Guided Lesson - Kimberly has $80. She wants to purchase a school bag for $16 and as many pairs of shoes as she can. Each pair of shoes is $8. Write an inequality for the number of school shoes she can purchase.
• Guided Lesson Explanation - Pay close attention to the graphing explanation it will save you time and time again.
• Practice Worksheet - This one may take students a lot time. Make sure to give them plenty of time and scrap paper.
• Matching Worksheet - If you are really good at writing and understanding inequalities, this will be a breeze for you.
• Applied Problems of Inequalities Five Worksheet Pack - I totally love these types of problems. Most people will call them riddles when they are just really calculated math.
• Triangular Inequalities Worksheet Five Pack - It is all about finding the longest side based on the measure of angles.
• Answer Keys - These are for all the unlocked materials above.

Homework Sheets

We start students off with the word problems and then we move to number lines.

• Homework 1 - Jacob gives his son $30 for chocolate. His son spends $16 on dark chocolate and spends the rest on white chocolate. Each white chocolate costs $7. Write an inequality for the number of white chocolate he can purchase.
• Homework 2 - Solve -0.3x – 4 > -9.4 and graph the solution on a number line.
• Homework 3 - Sarah has $80. She wants to purchase a school bag for $16 and as many pairs of shoes as she can. Each pair of shoes is $8. Write an inequality to find how many pairs of shoes she can purchase.

Practice Worksheets

The biggest problem here is for students to remember the difference between an open and closed inline arrow.

• Practice 1 - Solve 2x + 2 > 4 and graph the solution on a number line.
• Practice 2 - Brock has $23 to spend on cupcakes. He wants to buy an orange cupcake for $8 and spend the rest on pink cupcakes. Each pink cupcake costs $5. Write an inequality that can be used to determine the number of pink cupcakes Brock can buy.
• Practice 3 - Mary has $20 to spend. She buys lunch for $14 and spends the rest on banana biscuits. Each banana biscuit costs $3. How many banana biscuits did she buy?

Math Skill Quizzes

I couldn't fit any number line based questions in here, sorry!

• Quiz 1 - Margaret wants to purchase a caramel apple ($7) and water melon slice ($4). She spends the rest of her money on pizza. She has $19 to start. Each pizza costs $2. How many pizzas can she get?
• Quiz 2 - Aiden wants to buy some clothes for his birthday. He has $40. He purchases a white shirt for $14. He spends the rest of the money on black pants. Each pair of pants costs $8. Write an inequality for the number of pairs of pants he can purchase.
• Quiz 3 - Brooke goes to the market. She purchases a red rose flower for $10 and a lily for $8. She spends the rest of her money on white roses. She has $30 at the start. Each white rose costs $3. How many white roses can she get?

How to Write Word Problems as Inequalities

Do you feel like algebraic word problems are difficult? Don't worry; we'll help to make these word problems as easy as possible. The first and foremost, you need to follow a few steps that will help you solve algebraic word problems. If you stay consistent with this, it will become a habit quickly. Here are some habits you should get in when working with these types of problems:

Step 1) Slow Down and Focus - Read the entire problem thoroughly. Highlight important information and keywords that you think are needed to solve the problem. Those keywords will often present themselves as math operations and comparisons that will help us form and ultimately write our inequality.

Step 2) Determine the Present Conditions - Carefully identify the variables. If there are any values such as coefficients or constants make sure to state those as well. I find it helpful to create an itemized list of all of them and the values associated with them before going any further.

Step 3) Create an Inequality - Take your itemized list and then look for keywords that may indicate relationships between these elements. Some of the phrases you are looking for include:

at least – this indicates a relationship that can be defined as greater than or equal. We use this symbol to signify this: (≥)

less, lesser, less than – indicates a less than (<) relationship.

bigger, larger, or more than – signifies a greater than (>) relationship.

no more than - this indicates a relationship that can be defined as less than or equal. We use this symbol to signify this: (≤)

Once we understand the statement made by the inequality, we place the variable that indicates the condition that needs to be satisfied on one side of the comparison symbol and we arrange the remaining variables and constants on the other side, as stated in the word problem.

Step 4) Solve It For Missing Parts - You can rearrange an inequality much like an equation to solve for a variable. Just consider the compare symbol an equals symbol. Once you have your final answer, realize that inequalities do not give us an exact location of the solution, rather an idea of where the answer lies. Recheck and justify your answer. You can do this by seeing if a fixed value would satisfy the situation that is presented.

In a saving account, Sam deposited $400. She wants to have at least $100 in her account by the end of summer. She withdraws $15 every week for food and movie tickets.

Here is how you will write an inequality: First, make sure you highlight the keyword (at least), that will be written down within the inequality as a (≥). Thoroughly read and highlight any other information that you need when writing the inequality. We can identify that she starts with $400 and in the end needs to have $100 or more. We can then identify that every week $15 is being removed from the total. We can rewrite that as 15w, where w is equal to the number of weeks. Here, the variable is the number of weeks since that is what you don't know. Now generating the inequality will be easy; 400 - 15w ≥ 100. We can solve for the number of weeks through these steps:

400 - 15w ≥ 100 (Subtract 400 from both sides)

- 15w ≥ -300 (Divide by -15)

This tells us that Sam can live on this budget for 20 weeks.

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Number line.

• \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
• \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
• \mathrm{The\:sum\:of\:two\:numbers\:is\:249\:.\:Twice\:the\:larger\:number\:plus\:three\:times\:the\:smaller\:number\:is\:591\:.\:Find\:the\:numbers.}
• \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
• \mathrm{You\:deposit\:3000\:in\:an\:account\:earning\:2\%\:interest\:compounded\:monthly.\:How\:much\:will\:you\:have\:in\:the\:account\:in\:15\:years?}
• How do you solve word problems?
• To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
• How do you identify word problems in math?
• Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
• Is there a calculator that can solve word problems?
• Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
• What is an age problem?
• An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

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• Middle School Math Solutions – Equation Calculator Welcome to our new "Getting Started" math solutions series. Over the next few weeks, we'll be showing how Symbolab...

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Math Worksheets

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• Constant of Proportionality Worksheets
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Graphing Inequalities Worksheets (Single Variable)

Solving inequalities worksheets.

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Inequalities Worksheets

Are you looking for free math worksheets that will help your students develop and master real-life math skills?  The algebra worksheets below will introduce your students to solving inequalities and graphing inequalities.  As they take a step-by-step approach to solving inequalities, they will also practice other essential algebra skills like using inverse operations to solve equations.

Solving Inequalities Worksheet 1 – Here is a twelve problem worksheet featuring simple one-step inequalities.  Use inverse operations or mental math to solve for x . Solving Inequalities Worksheet 1 RTF Solving Inequalities Worksheet 1 PDF Preview Solving Inequalities Worksheet 1  in Your Browser View Answers 

Solving Inequalities Worksheet 2 – Here is a twelve problem worksheet featuring simple one-step inequalities.  Use inverse operations or mental math to solve for x . Solving Inequalities Worksheet 2 RTF Solving Inequalities Worksheet 2 PDF Preview Solving Inequalities Worksheet 2 in Your Browser View Answers

Solving Inequalities Worksheet 3 – Here is a twelve problem worksheet featuring two-step inequalities.  Use inverse operations or mental math to solve for x . Solving Inequalities Worksheet 3 RTF Solving Inequalities Worksheet 3 PDF Preview Solving Inequalities Worksheet 3 in Your Browser View Answers

Solving Inequalities Worksheet 4 – Here is a twelve problem worksheet featuring one-step inequalities.  Use inverse operations or mental math to solve for x . Solving Inequalities Worksheet 4 RTF Solving Inequalities Worksheet 4 PDF Preview Solving Inequalities Worksheet 4 in Your Browser View Answers

Solving Inequalities Worksheet 5 – Here is a twelve problem worksheet featuring two-step inequalities.  Use inverse operations or mental math to solve for x . Solving Inequalities Worksheet 5 RTF Solving Inequalities Worksheet 5 PDF Preview Solving Inequalities Worksheet 5 in Your Browser View Answers

Graphing Inequalities Workheet 1 –  Here is a 15 problem worksheet where students will graph simple inequalities like  “ x < -2″  on a number line. Graphing Inequalities Worksheet 1 RTF Graphing Inequalities 1 PDF View Answers

Graphing Inequalities Workheet  2 –  Here is a 15 problem worksheet where students will graph simple inequalities like  “ x < -2″  and “ -x > 2″  on a number line.  Be careful, you may have to reverse one or two of the inequality symbols to get the correct solution set. Graphing Inequalities 2 RTF Graphing Inequalities 2 PDF View Answers

Graphing Inequalities Workheet  3 –  Here is a 12 problem worksheet where students will both  solve  inequalities and  graph  inequalities on a number line.  This set features one-step addition inequalities such as   “x + 5 > 7”. Graphing Inequalities 3 RTF Graphing Inequalities 3 PDF View Answers

Graphing Inequalities Workheet  4 –  Here is a 12 problem worksheet where students will both  solve  inequalities and  graph  inequalities on a number line.  This set features one-step addition and subtraction inequalities such as   “5 + x > 7”  and  “x – 3″ < 21”. Graphing Inequalities 4 RTF Graphing Inequalities 4 PDF View Answers

Graphing Inequalities Workheet  5 –   Here is a 12 problem worksheet where students will both  solve  inequalities and  graph  inequalities on a number line.  This set features two-step addition inequalities such as   “2x + 5 > 15” . Graphing Inequalities 5 RTF Graphing Inequalities 5 PDF View Answers

Graphing Inequalities Workheet  6 –  Here is a 12 problem worksheet where students will both  solve  inequalities and  graph  inequalities on a number line.  This set features two-step addition and subtraction inequalities such as   “2x + 5 > 15”  and “ 4x -2 = 14. Graphing Inequalities 6 RTF Graphing Inequalities 6 PDF View Answers

Absolute Value Inequality Worksheets (Single Variable)

Absolute Value Inequality Worksheet 1 –  Here is a 9 problem worksheet where you will find the solution set of absolute value inequalities.  These are one-step inequalities with mostly positive integers. Absolute Value Equations Worksheet 1 RTF Absolute Value Equations Worksheet 1 PDF View Answers

Absolute Value Inequality Worksheet 2 –  Here is a 9 problem worksheet where you will find the solution set of absolute value inequalities.   These are one-step inequalities where you’ll need to use all of your inverse operations knowledge. Absolute Value Equations Worksheet 2 RTF Absolute Value Equations Worksheet 2 PDF View Answers

Absolute Value Inequality Worksheet 3 –  Here is a 9 problem worksheet where you will find the solution set of absolute value inequalities.  These are two-step inequalities where you’ll need to use all of your inverse operations knowledge. Absolute Value Equations Worksheet 3 RTF Absolute Value Equations Worksheet 3 PDF View Answers

Absolute Value Inequality Worksheet 4 –  Here is a 9 problem worksheet where you will find the solution set of absolute value inequalities.  These are two-step inequalities that can get quite complicated.  A nice challenge for your higher-level learners. Absolute Value Equations Worksheet 4 RTF Absolute Value Equations Worksheet 4 PDF View Answers

20 Comments

This web is good

Thanks for your support.

i like it. Its very helpful.

I appreciate the feedback. Good luck with your math endeavors!

I like this website. It is very helpful for students.

Thanks. I’ll be adding more worksheets soon.

Interesting questions. Very good.

Thanks. I’m glad you enjoyed them.

This is a great site! Thanks so much for helping me teach this concept to my 5th graders!

Mr. Colwell

I’m glad that I could help. Thanks for visiting the site and come back often!

Kaity Fanara

Very helpful, thanks!

You’re very welcome. I plan to add some Graphing Inequalities Worksheets soon. Thanks for your support.

c’moon! so easy give me something like, ( m-2 ) x2 – (m+5) x + m-8 = 0, if it has 2 equal roots, what’s m? i need this kind, where can i find

That’s a pretty good one. Let me see what I can do.

Mr. Lindugani Mlilile

Thanks for your website which helps me teach my students of form one in Tanzania. I always teach my students on how solve the topic of inequality. Please add more topic so that my students will continue to enjoys!

It’s nice to hear from our international visitors. I’m always adding new content. Check back often!

It is helpful but I can’t see the answer sheet for all of them.

wish their was some fractions inequalities and equalities

however work sheets have helped me tremendously just the one little flaw of not having fraction problems.

I LOVE THIS WEBSITE. I USE IT EVERY DAY TO STUDY FOR TEST OR QUIZ FOR SCHOOL.

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Could helicopter parenting and a decline in ‘free play’ be causing the youth mental health crisis?

Boston college professor peter gray says screen time is less of a problem than people think..

When Peter Gray remarried and became a stepfather to two small children in the early aughts, he made a discovery that surprised him. Most children were no longer allowed to play outdoors on their own.

The Boston College evolutionary biologist soon noticed other changes that highlighted just how much childhood had transformed since his first son, Scott, graduated from high school in the late 1980s. Once they entered elementary school, his stepchildren spent more time in the classroom and on homework at younger ages. Their after-school hours were overscheduled with adult-supervised sports and activities.

Even before smartphones ushered in the age of the modern “screenager,” it seemed to him, unstructured play time — a staple of most childhoods since the dawn of humanity — had almost completely disappeared.

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“The nature of childhood itself was changing,” he said. “And changing profoundly.”

In the wake of the COVID-19 pandemic, as public attention has focused on the teen mental health crisis, experts and commentators have increasingly linked soaring rates of anxiety, depression, and suicides to the rise of smartphones and social media. Gray has emerged in recent years as a leading advocate for an alternative theory that is quietly gaining ground among experts. Could the disappearance of free play, and not teenagers’ obsessions with their phones, be the key factor driving the teen mental health crisis?

In a recent paper, published in The Journal of Pediatrics late last year, Gray and his colleagues made the case by drawing from a voluminous body of evidence spanning developmental psychology, neuroscience, evolutionary biology, and other fields. While it may be true that the prevalence of anxiety, depression, and suicide among children and teenagers appears to have risen in tandem with the use of smartphones and social media, they concluded that teen and child mental health has actually been on the decline for at least five decades. That period coincides with the decline in opportunities “for children and teens to play, roam, and engage in other activities independent of direct oversight and control by adults, ” they wrote.

“Everything that I know about play suggests that if you take play away from children, there’s going to be negative consequences,” said Gray, whose 2013 book “Free to Learn” argued that free play is the primary means by which children develop resilience .

In 2019, nearly one in five children between the ages of 3 and 17 in the United States had a diagnosed mental, emotional, developmental, or behavioral disorder, up by more than 40 percent since 2009, according to a 2021 Surgeon General advisory. Between 2008 and 2020, the rates of death by suicide for Americans between the ages of 12 and 17 rose by 70 percent.

In the fall of 2021, the American Academy of Pediatrics, American Academy of Child and Adolescent Psychiatry, and Children’s Hospital Association issued a joint statement declaring child and adolescent mental health a “national emergency.” Soon after, US Surgeon General Vivek H. Murthy issued a rare public health advisory, calling youth mental health “the defining public health issue of our time.”

But the surgeon general has blamed the crisis on social media and on the amount of time children and adolescents spend online. Those links are also one of the key takeaways from “ The Anxious Generation , ” a recently published bestseller by NYU social psychologist Jonathan Haidt . In his book, Haidt, a longtime Gray collaborator, also laments the decline of the “play-based childhood.” He chronicles its replacement with a “phone-based childhood” and details what he calls a “great rewiring,” a state of affairs that is interfering with the healthy social and neurological development of the nation’s children and fueling an epidemic of addiction, loneliness, attention fragmentation, and mental illness.

Gray said he read early copies of Haidt’s book and urged him, unsuccessfully, to change its focus.

Gray argues screens may have actually helped to attenuate the negative affects of the decline in free play on youth mental well-being. He suggests the rise of collaborative online gaming in the early 2000s coincided with a temporary reversal in the rate of youth mental health problems. (He believes the wide adoption of standardized testing, the common core, and other changes in American schools caused the number to rise once again).

“My objection to the book is that it feeds into everybody’s prejudice,” Gray said. “It doesn’t matter that he says it’s play also, because that’s not what people are going to pay attention to with this book. The first chapters are all on social media. That’s what’s going to resonate. The book is selling because of the screens.”

Haidt did not respond to a request for comment.

Lenore Skenazy, president of Let Grow , a New York-based nonprofit that bills itself as leading the “movement for childhood independence,” has been listening to Gray and Haidt debate the relative merits and drawbacks of video games for months, and her opinion falls somewhere in between. But she, too, worries that Haidt’s message about play is not getting the attention it deserves in media coverage of the book.

“You can’t just take phones away,” she said. “You have to give kids back what we have taken out of their lives, which is the autonomy to be part of the world without constant supervision.”

Skenazy, a New York-based journalist and the author of the book “ Free Range Kids, ” rose to national prominence in 2009, when she penned a viral column announcing that she had left her 9-year-old son alone in Bloomingdales and allowed him to make his way home alone on the bus and subway. She teamed up with Gray; Haidt, who had previously written on the psychological fragility of college students; and investor turned philanthropist and campus free speech advocate Dan Shuchman to form the nonprofit in 2017.

The organization has been working with schools around the nation to form “ free play clubs ” that allow children to play uninhibited and without phones before or after school. It has also been lobbying state legislators to pass laws aimed at promoting what it calls “reasonable childhood independence,” by protecting parents against neglect and criminal charges for allowing children to travel to or from school or nearby locations by bicycle or on foot, playing outdoors, or remaining at home alone for a “reasonable” amount of time. Eight states —including Utah, Oklahoma, Texas, Colorado, Virginia, Illinois, Connecticut, and Montana — have since passed such laws.

A growing body of evidence has emerged from scientific labs in recent years suggesting that “free” play isn’t just fun, it’s a crucial tool for normal development. One hint of its evolutionary importance is its universality. Scientists have observed play, which can be defined as purposeless activity engaged in purely for fun, in dogs, cats, monkeys, crocodiles, bears, fish — even spiders and bumblebees. Play, they have shown, allows developing animals to experiment with new capabilities, to improvise, and test their limits and abilities in a safe, protected environment. In humans, it allows children to use their imagination, express their creativity, and learn to deal with and respond to the unexpected.

Peer-to-peer play is also important for socialization. It’s how, Marc Bekoff, a professor of ecology and evolutionary biology at the University of Colorado Boulder, puts it, animals “learn how to behave like a card-carrying member of their species.” Play may even be crucial to shaping the developing brain, by strengthening neurons that are important and “pruning” the ones that are unused. In one recent Canadian study, researchers showed that the brains of rats that were reared without play experienced far less pruning in areas of the brain essential for executive functions such as emotional regulation, sociability, motivation, and cognitive processing. In later years, they lacked impulse control and were unable to respond appropriately to potential mates.

To make the case for play clubs, Gray helped design a systematic research study that is being run by Jessica Black, a professor at the Boston College School of Social Work, in elementary schools across New Hampshire. Selected schools have committed to establishing a “play club,” offering an hour of free play to children in kindergarten through fifth grade either before or after school. The children who participate will undergo a wide variety of psychological tests designed to measure psychological well-being, and other metrics. Their outcomes will be compared with a control group of schools without it.

“Play is how children naturally develop,” Gray said. “It’s how they learn to push the limits and deal with fear, to solve problems, and to deal with anger and get along with playmates. Take it away, and they’re just not going to be prepared for the stresses of life.”

Adam Piore can be reached at [email protected] .