problem solving linear equations worksheet

Find here an unlimited supply of printable worksheets for solving linear equations, available as both PDF and html files. You can customize the worksheets to include one-step, two-step, or multi-step equations, variable on both sides, parenthesis, and more. The worksheets suit and courses (grades 6-9).

You can choose from SEVEN basic types of equations, ranging from simple to complex, explained below (such as one-step equations, variable on both sides, or having to use the distributive property). Customize the worksheets using the below.

Each worksheet is randomly generated and thus unique. The and is placed on the second page of the file.

You can generate the worksheets — both are easy to print. To get the PDF worksheet, simply push the button titled " " or " ". To get the worksheet in html format, push the button " " or " ". This has the advantage that you can save the worksheet directly from your browser (choose File → Save) and then in Word or other word processing program.

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Key to Algebra offers a unique, proven way to introduce algebra to your students. New concepts are explained in simple language, and examples are easy to follow. Word problems relate algebra to familiar situations, helping students to understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively before formal solutions are introduced. Students begin their study of algebra in Books 1-4 using only integers. Books 5-7 introduce rational numbers and expressions. Books 8-10 extend coverage to the real number system.

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Linear Equation Worksheets (Distributive Property)

Related Topics: More Math Worksheets More Grade 7 Math Lessons Grade 7 Math Worksheets

There are five sets of solving linear equation worksheets:

• Solve linear equations (1-step equations)
• Solve linear equations (2-step equations)
• Solve linear equations (combine like terms)
• Solve linear equations (distributive property & combine like terms)
• Solve linear equations (fractions)

Examples, solutions, videos, and worksheets to help Grade 6 and Grade 7 students learn how to solve linear equations by using the distributive property and combining like terms.

How to solve linear equations (distributive property & combining like terms)?

There are three sets of solving linear equations worksheets using distributive property & combining like terms.

• Solve linear equations (variables on one side, positive coefficients).
• Solve linear equations (variables on one side, negative coefficients).
• Solve linear equations (variables on both sides).

You can follow these steps to solve a linear equation:

• Use the distributive property and combine like terms, if applicable.
• Multiply each term inside the parentheses by the number or variable outside the parentheses.
• Combine the like terms that were created by the distribution.
• Isolate the variable term. Perform inverse operations to move all other terms to the opposite side of the equation.
• Simplify the equation further, if necessary, until you have the variable term isolated on one side of the equation.
• Solve for the variable by performing the necessary operations to isolate it.
• Check your solution by substituting the value you found back into the original equation and verifying that both sides are equal.

For example, 3x + 3(2x + 3) = 54 3x + 6x + 9 = 54 9x + 9 = 54 9x = 54 x = 5

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Linear Equations Worksheets .

More Linear Equation Worksheets (Distributive Property & Combine Like Terms)

Printable (Answers on the second page.) Linear Equations Worksheet #1 (variables on one side, positive coefficients) Linear Equations Worksheet #2 (variables on one side, negative coefficients) Linear Equations Worksheet #3 (variables on both sides)

Online or Generated Combine like Terms (Sprint) Solve by Combining Like Terms Solve Equations with the Variable on Both Sides Solve Equations by Distributive Property Solve Multi-Step Equations 1 Solve Multi-Step Equations 2 Solve Word Problems using Algebra

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Linear Equation Worksheets

These worksheets help reinforce students’ understanding of solving and graphing linear equations. The worksheets contain a variety of problems and exercises involving linear equations, ranging from basic to more complex scenarios. Students are tasked with solving equations for a single variable, identifying slope and intercepts, graphing linear equations on coordinate planes, and interpreting the meaning of solutions in real-world contexts. Linear Equation Worksheets provide valuable practice opportunities for students to hone their algebraic skills, build confidence in solving linear equations, and develop proficiency in graphing and interpreting linear relationships.

A Variable on Both Sides | Graphing Linear Equations

Slope | Growing Patterns | Speed, Time, and Distance

Two-Step Linear Equations | Linear Equation Word Problems

What Are Linear Equations?

Linear equations are fundamental mathematical expressions that describe the relationship between two variables in a straight line. They are among the simplest and most important equations in algebra and are widely used in various fields such as physics, engineering, economics, and social sciences. A linear equation can be expressed in the form:

y is the dependent variable, representing the output or value being measured.

x is the independent variable, representing the input or variable that is manipulated.

m is the slope of the line, indicating the rate of change or steepness of the line.

b is the y-intercept, representing the point where the line crosses the y-axis when x = 0

Linear equations can also be written in different forms to emphasize different aspects of the equation. One common form is the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. This form is particularly useful for graphing linear equations since it directly provides the slope and y-intercept of the line.

Another form is the standard form A x + B y = C, where A, B, and C are constants. In this form, the coefficients A and B determine the slope of the line, while C determines the y-intercept when the equation is rearranged into slope-intercept form.

Linear equations can also be expressed in point-slope form y – y 1 = m(x – x 1 ), where m is the slope of the line, and (x 1 , y 1 )is a point on the line. This form is useful for finding the equation of a line given its slope and a point it passes through.

The graph of a linear equation is a straight line on a Cartesian coordinate plane. The slope of the line determines its steepness: a positive slope indicates a line that rises as x increases, while a negative slope indicates a line that falls as x increases. A slope of zero results in a horizontal line, while an undefined slope corresponds to a vertical line.

Linear equations are used to model various real-world phenomena, such as the relationship between distance and time in motion problems, the relationship between supply and demand in economics, or the trajectory of a projectile in physics. They provide a powerful tool for analyzing and predicting behavior in situations where there is a linear relationship between two variables. Overall, linear equations serve as a foundational concept in algebra and play a crucial role in numerous applications across different fields of study.

What Are The Parts of a Linear Equation?

A linear equation is a mathematical expression that represents the relationship between two variables in a straight line. Let’s break down the different parts of a linear equation:

• Variables: In a linear equation, typically denoted as y = mx + b, there are two variables:

x: The independent variable represents the input or the variable that can be manipulated or controlled.

y: The dependent variable represents the output or the variable whose value depends on the value of the independent variable.

• Slope (m): The slope of a line is a measure of its steepness or incline. It indicates how much the dependent variable (y) changes for a given change in the independent variable (x).

A positive slope (m > 0) indicates that as the value of x increases, the value of y also increases, resulting in an upward sloping line.

A negative slope (m < 0) indicates that as the value of x increases, the value of y decreases, resulting in a downward sloping line.

A slope of zero (m = 0) results in a horizontal line where y remains constant regardless of changes in x.

An undefined slope occurs when the line is vertical, meaning that x remains constant while y can vary.

• Y-intercept (b): The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x is equal to zero.

It is denoted as the ordered pair (0, b), where b is the y-coordinate of the point of intersection with the y-axis.

The y-intercept determines the initial value or the starting point of the line on the y-axis.

Equation Forms: Linear equations can be represented in various forms, each highlighting different aspects of the equation.

Slope-intercept form (y = mx + b): This form directly reveals the slope (m) and y-intercept (b) of the line.

Standard form (A x + B y = C): In this form, A, B, and C are constants, and it’s useful for easily identifying the x-intercept and y-intercept of the line.

Point-slope form (y – y 1 = m (x -x 1 )) : This form allows the equation to be written given a point (x 1 , y 1 )on the line and its slope (m).

Understanding the different parts of a linear equation allows us to interpret and manipulate equations to represent relationships between variables graphically and algebraically. It also enables us to solve problems, analyze data, and make predictions in various real-world contexts where linear relationships exist.

Linear Equation Worksheets. Free worksheets with answer keys

Enjoy these free printable worksheets . Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.

• Mixed Problems on Writing Equations of Lines
• Slope Intercept Form Worksheet
• Standard Form Worksheet
• Point Slope Worksheet
• Write Equation of Line From the Slope and 1 Point
• Write Equation of Line From Two Points
• Equation of Line Parallel to Another Line and Through a Point
• Equation of Line Perpendicular to Another Line and Through a Point
• Slope of a Line
• Perpendicular Bisector of Segment
• Write Equation of Line Mixed Review
• Word Problems

Ultimate Math Solver (Free) Free Algebra Solver ... type anything in there!

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Word Problems Linear Equations

Andymath.com features free videos, notes, and practice problems with answers! Printable pages make math easy. Are you ready to be a mathmagician?

\(\textbf{1)}\) Joe and Steve are saving money. Joe starts with $105 and saves $5 per week. Steve starts with $5 and saves $15 per week. After how many weeks do they have the same amount of money? Show Equations \(y= 5x+105,\,\,\,y=15x+5\) Show Answer 10 weeks ($155)

\(\textbf{2)}\) mike and sarah collect rocks. together they collected 50 rocks. mike collected 10 more rocks than sarah. how many rocks did each of them collect show equations \(m+s=50,\,\,\,m=s+10\) show answer mike collected 30 rocks, sarah collected 20 rocks., \(\textbf{3)}\) in a classroom the ratio of boys to girls is 2:3. there are 25 students in the class. how many are girls show equations \(b+g=50,\,\,\,3b=2g\) show answer 15 girls (10 boys), \(\textbf{4)}\) kyle makes sandals at home. the sandal making tools cost $100 and he spends $10 on materials for each sandal. he sells each sandal for $30. how many sandals does he have to sell to break even show equations \(c=10x+100,\,\,\,r=30x\) show answer 5 sandals ($150), \(\textbf{5)}\) molly is throwing a beach party. she still needs to buy beach towels and beach balls. towels are $3 each and beachballs are $4 each. she bought 10 items in total and it cost $34. how many beach balls did she get show equations show answer 4 beachballs (6 towels), \(\textbf{6)}\) anna volunteers at a pet shelter. they have cats and dogs. there are 36 pets in total at the shelter, and the ratio of dogs to cats is 4:5. how many cats are at the shelter show equations \(c+d=40,\,\,\,5d=4c\) show answer 20 cats (16 dogs), \(\textbf{7)}\) a store sells oranges and apples. oranges cost $1.00 each and apples cost $2.00 each. in the first sale of the day, 15 fruits were sold in total, and the price was $25. how many of each type of frust was sold show equations \(o+a=15,\,\,\,1o+2a=25\) show answer 10 apples and 5 oranges, \(\textbf{8)}\) the ratio of red marbles to green marbles is 2:7. there are 36 marbles in total. how many are red show equations \(r+g=36,\,\,\,7r=2g\) show answer 8 red marbles (28 green marbles), \(\textbf{9)}\) a tennis club charges $100 to join the club and $10 for every hour using the courts. write an equation to express the cost \(c\) in terms of \(h\) hours playing tennis. show equation the equation is \(c=10h+100\), \(\textbf{10)}\) emma and liam are saving money. emma starts with $80 and saves $10 per week. liam starts with $120 and saves $6 per week. after how many weeks will they have the same amount of money show equations \(e = 10x + 80,\,\,\,l = 6x + 120\) show answer 10 weeks ($180 each), \(\textbf{11)}\) mark and lisa collect stamps. together they collected 200 stamps. mark collected 40 more stamps than lisa. how many stamps did each of them collect show equations \(m + l = 200,\,\,\,m = l + 40\) show answer mark collected 120 stamps, lisa collected 80 stamps., \(\textbf{12)}\) in a classroom, the ratio of boys to girls is 3:5. there are 40 students in the class. how many are boys show equations \(b + g = 40,\,\,\,5b = 3g\) show answer 15 boys (25 girls), \(\textbf{13)}\) lisa is selling handmade jewelry. the materials cost $60, and she sells each piece for $20. how many pieces does she have to sell to break even show equations \(c=60,\,\,\,r=20x\) show answer 3 pieces, \(\textbf{14)}\) tom is buying books and notebooks for school. books cost $15 each, and notebooks cost $3 each. he bought 12 items in total, and it cost $120. how many notebooks did he buy show equations \(b + n = 12,\,\,\,15b+3n=120\) show answer 5 notebooks (7 books), \(\textbf{15)}\) emily volunteers at an animal shelter. they have rabbits and guinea pigs. there are 36 animals in total at the shelter, and the ratio of guinea pigs to rabbits is 4:5. how many guinea pigs are at the shelter show equations \(r + g = 36,\,\,\,5g=4r\) show answer 16 guinea pigs (20 rabbits), \(\textbf{16)}\) mike and sarah are going to a theme park. mike’s ticket costs $40, and sarah’s ticket costs $30. they also bought $20 worth of food. how much did they spend in total show equations \(m + s + f = t,\,\,\,m=40,\,\,\,s=30,\,\,\,f=20\) show answer they spent $90 in total., \(\textbf{17)}\) the ratio of red marbles to blue marbles is 2:3. there are 50 marbles in total. how many are blue show equations \(r + b = 50,\,\,\,3r=2b\) show answer 30 blue marbles (20 red marbles), \(\textbf{18)}\) a pizza restaurant charges $12 for a large pizza and $8 for a small pizza. if a customer buys 5 pizzas in total, and it costs $52, how many large pizzas did they buy show equations \(l + s = 5,\,\,\,12l+8s=52\) show answer they bought 3 large pizzas (2 small pizzas)., \(\textbf{19)}\) the area of a rectangle is 48 square meters. if the length is 8 meters, what is the width of the rectangle show equations \(a=l\times w,\,\,\,l=8,\,\,\,a=48\) show answer the width is 6 meters., \(\textbf{20)}\) two numbers have a sum of 50. one number is 10 more than the other. what are the two numbers show equations \(x+y=50,\,\,\,x=y+10\) show answer the numbers are 30 and 20., \(\textbf{21)}\) a store sells jeans for $40 each and t-shirts for $20 each. in the first sale of the day, they sold 8 items in total, and the price was $260. how many of each type of item was sold show equations \(j+t=8,\,\,\,40j+20t=260\) show answer 5 jeans and 3 t-shirts were sold., \(\textbf{22)}\) the ratio of apples to carrots is 3:4. there are 28 fruits in total. how many are apples show equations \(\)a+c=28,\,\,\,4a=3c show answer there are 12 apples and 16 carrots., \(\textbf{23)}\) a phone plan costs $30 per month, and there is an additional charge of $0.10 per minute for calls. write an equation to express the cost \(c\) in terms of \(m\) minutes. show equation the equation is \(\)c=30+0.10m, \(\textbf{24)}\) a triangle has a base of 8 inches and a height of 6 inches. calculate its area. show equations \(a=0.5\times b\times h,\,\,\,b=8,\,\,\,h=6\) show answer the area is 24 square inches., \(\textbf{25)}\) a store sells shirts for $25 each and pants for $45 each. in the first sale of the day, 4 items were sold, and the price was $180. how many of each type of item was sold show equations \(t+p=4,\,\,\,25t+45p=180\) show answer 0 shirts and 4 pants were sold., \(\textbf{26)}\) a garden has a length of 12 feet and a width of 10 feet. calculate its area. show equations \(a=l\times w,\,\,\,l=12,\,\,\,w=10\) show answer the area is 120 square feet., \(\textbf{27)}\) the sum of two consecutive odd numbers is 56. what are the two numbers show equations \(x+y=56,\,\,\,x=y+2\) show answer the numbers are 27 and 29., \(\textbf{28)}\) a toy store sells action figures for $15 each and toy cars for $5 each. in the first sale of the day, 10 items were sold, and the price was $110. how many of each type of item was sold show equations \(a+c=10,\,\,\,15a+5c=110\) show answer 6 action figures and 4 toy cars were sold., \(\textbf{29)}\) a bakery sells pie for $2 each and cookies for $1 each. in the first sale of the day, 14 items were sold, and the price was $25. how many of each type of item was sold show equations \(p+c=14,\,\,\,2p+c=25\) show answer 11 pies and 3 cookies were sold., \(\textbf{for 30-33}\) two car rental companies charge the following values for x miles. car rental a: \(y=3x+150 \,\,\) car rental b: \(y=4x+100\), \(\textbf{30)}\) which rental company has a higher initial fee show answer company a has a higher initial fee, \(\textbf{31)}\) which rental company has a higher mileage fee show answer company b has a higher mileage fee, \(\textbf{32)}\) for how many driven miles is the cost of the two companies the same show answer the companies cost the same if you drive 50 miles., \(\textbf{33)}\) what does the \(3\) mean in the equation for company a show answer for company a, the cost increases by $3 per mile driven., \(\textbf{34)}\) what does the \(100\) mean in the equation for company b show answer for company b, the initial cost (0 miles driven) is $100., \(\textbf{for 35-39}\) andy is going to go for a drive. the formula below tells how many gallons of gas he has in his car after m miles. \(g=12-\frac{m}{18}\), \(\textbf{35)}\) what does the \(12\) in the equation represent show answer andy has \(12\) gallons in his car when he starts his drive., \(\textbf{36)}\) what does the \(18\) in the equation represent show answer it takes \(18\) miles to use up \(1\) gallon of gas., \(\textbf{37)}\) how many miles until he runs out of gas show answer the answer is \(216\) miles, \(\textbf{38)}\) how many gallons of gas does he have after 90 miles show answer the answer is \(7\) gallons, \(\textbf{39)}\) when he has \(3\) gallons remaining, how far has he driven show answer the answer is \(162\) miles, \(\textbf{for 40-42}\) joe sells paintings. each month he makes no commission on the first $5,000 he sells but then makes a 10% commission on the rest., \(\textbf{40)}\) find the equation of how much money x joe needs to sell to earn y dollars per month. show answer the answer is \(y=.1(x-5,000)\), \(\textbf{41)}\) how much does joe need to sell to earn $10,000 in a month. show answer the answer is \($105,000\), \(\textbf{42)}\) how much does joe earn if he sells $45,000 in a month show answer the answer is \($4,000\), see related pages\(\), \(\bullet\text{ word problems- linear equations}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- averages}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- consecutive integers}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- distance, rate and time}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- break even}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- ratios}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- age}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- mixtures and concentration}\) \(\,\,\,\,\,\,\,\,\), linear equations are a type of equation that has a linear relationship between two variables, and they can often be used to solve word problems. in order to solve a word problem involving a linear equation, you will need to identify the variables in the problem and determine the relationship between them. this usually involves setting up an equation (or equations) using the given information and then solving for the unknown variables . linear equations are commonly used in real-life situations to model and analyze relationships between different quantities. for example, you might use a linear equation to model the relationship between the cost of a product and the number of units sold, or the relationship between the distance traveled and the time it takes to travel that distance. linear equations are typically covered in a high school algebra class. these types of problems can be challenging for students who are new to algebra, but they are an important foundation for more advanced math concepts. one common mistake that students make when solving word problems involving linear equations is failing to set up the problem correctly. it’s important to carefully read the problem and identify all of the relevant information, as well as any given equations or formulas that you might need to use. other related topics involving linear equations include graphing and solving systems. understanding linear equations is also useful for applications in fields such as economics, engineering, and physics., about andymath.com, andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. if you have any requests for additional content, please contact andy at [email protected] . he will promptly add the content. topics cover elementary math , middle school , algebra , geometry , algebra 2/pre-calculus/trig , calculus and probability/statistics . in the future, i hope to add physics and linear algebra content. visit me on youtube , tiktok , instagram and facebook . andymath content has a unique approach to presenting mathematics. the clear explanations, strong visuals mixed with dry humor regularly get millions of views. we are open to collaborations of all types, please contact andy at [email protected] for all enquiries. to offer financial support, visit my patreon page. let’s help students understand the math way of thinking thank you for visiting. how exciting.

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Linear Equations

On these printable worksheets, students will practice solving, finding x and y intercepts, and graphing linear equations.

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About these 15 worksheets.

These worksheets help students practice and master the process of solving for variables in algebraic equations. These worksheets are designed with a variety of formats and problem types to engage students and reinforce their understanding of algebraic principles. The worksheets guide students through the fundamental skills needed to manipulate and simplify equations, ultimately solving for unknowns. They often incorporate creative elements, such as mazes, matching exercises, or themed designs, to keep the practice engaging and dynamic.

One common type of problem found on these worksheets is the straightforward linear equation. These problems focus on basic one-step or two-step equations, where students are required to isolate the variable by performing inverse operations. For example, students may need to add, subtract, multiply, or divide both sides of an equation to balance it and solve for the unknown. These types of problems are crucial because they form the foundation for more complex algebraic concepts. By repeatedly practicing these steps, students solidify their understanding of the equality principle and learn how to reverse operations to simplify equations.

In addition to traditional linear equations, many of these worksheets also feature problems that involve negative numbers, fractions, and decimals. This inclusion helps students develop fluency in handling a variety of number types, which is critical as they progress in their math studies. Solving equations that involve fractions requires students to multiply by the reciprocal or find common denominators, while working with decimals involves careful attention to place value. These challenges enhance a student’s precision and calculation skills, as even small errors in handling fractions or decimals can lead to incorrect solutions.

Another engaging format found on these worksheets is the maze or path-solving activity. In these exercises, students must follow a sequence of correct answers to navigate through a maze. Each correct solution leads them to the next step in the maze, while incorrect answers might lead them astray. This format adds a layer of fun to equation solving while reinforcing accuracy and critical thinking. Students are motivated to double-check their answers to ensure they’re on the right path, which encourages attention to detail. These mazes are an excellent way to build both speed and precision in solving equations.

Many worksheets also incorporate matching or fill-in-the-blank exercises where students solve an equation and then match their solution with a corresponding answer. This type of exercise can be particularly useful for self-checking, as it provides immediate feedback. If a student’s solution doesn’t match any of the available options, they know to revisit their work and look for errors. This format fosters independence and allows students to take ownership of their learning process, developing problem-solving skills that extend beyond the classroom.

These worksheets are designed with a theme or a creative twist, such as solving for variables in a secret message. In these problems, each correct answer corresponds to a letter, and when all the problems are solved, the letters spell out a hidden word or phrase. This type of worksheet adds an element of surprise and fun, keeping students engaged and motivated to complete the task. The process of solving each equation remains the same, but the added challenge of uncovering a hidden message makes the practice more enjoyable and rewarding.

Another important aspect of these worksheets is that they often include a mix of equation types to ensure students are exposed to a broad range of problem-solving scenarios. For instance, students might encounter equations with variables on both sides, which require them to combine like terms and move all variable terms to one side of the equation. These problems teach students how to simplify more complex algebraic expressions and develop a deeper understanding of how to manipulate equations to find solutions.

Equations involving parentheses and the distributive property are also commonly featured. These problems require students to expand expressions by applying the distributive property before solving the equation. This introduces another layer of complexity, as students must remember to correctly distribute terms across all elements within the parentheses. These exercises reinforce the importance of following the correct order of operations and provide practice in breaking down more complex expressions into manageable steps.

The skills taught through these worksheets are foundational for success in higher-level math. By practicing with these worksheets, students develop a strong understanding of how to manipulate algebraic expressions and solve for unknowns, a skill that is critical for more advanced math topics such as systems of equations, quadratic equations, and functions. The variety of problems and formats ensures that students are not only practicing routine calculations but also developing flexibility in their problem-solving approaches.

These worksheets promote a growth mindset by encouraging students to view mistakes as learning opportunities. With immediate feedback from matching or maze activities, students can identify errors and correct their understanding, reinforcing the idea that persistence and practice lead to improvement. This mindset is crucial for building confidence in math, as it teaches students that challenges are an integral part of the learning process.

Worksheet on Word Problems on Linear Equation

In worksheet on word problems on linear equation in one variable student can practice different types of equation problems.

1.  Convert the following statements into equations.  (a) 5 added to a number is 9.  (b) 3 subtracted from a number is equal to 12.  (c) 5 times a number decreased by 2 is 4.  (d) 2 times the sum of the number x and 7 is 13.  2.  A number is 12 more than the other. Find the numbers if their sum is 48.  3.  Twice the number decreased by 22 is 48. Find the number.  4.  Seven times the number is 36 less than 10 times the number. Find the number.  5.  4/5 of a number is more than 3/4 of the number by 5 . Find the number. 

6. The sum of two consecutive even numbers is 38. Find the numbers. 7. The sum of three consecutive odd numbers is 51. Find the numbers. 8. Rene is 6 years older than her younger sister. After 1 0 years, the sum of their ages will be 50 years. Find their present ages. 9. The length of a rectangle is 10 m more than its breadth. If the perimeter of rectangle is 80 m, find the dimensions of the rectangle. 10. A 300 m long wire is used to fence a rectangular plot whose length is twice its width. Find the length and breadth of the plot. 11. The denominator of a fraction is greater than the numerator by 8. If the numerator is increased by 17 and denominator is decreased by 1, the number obtained is 3/2, find the fraction. 12. A sum of $2700 is to be given in the form of 63 prizes. If the prize is of either $100 or $25, find the number of prizes of each type. 13. In a class of 42 students, the number of boys is 2/5 of the girls. Find the number of boys and girls in the class. 14. Among the two supplementary angles, the measure of the larger angle is 36° more than the measure of smaller. Find their measures. 15. My mother is 12 years more than twice my age. After 8 years, my mother’s age will be 20 years less than three times my age. Find my age and my mother’s age. 16. In an isosceles triangle, the base angles are equal and the vertex angle is 80°. Find the measure of the base angles. 17. Adman’s father is 49 years old. He is 5 years older than four times Adman’s age. What is Adman’s age? 18. The cost of a pencil is 25 cents more than the cost of a eraser. If the cost of 8 pencils and 10 erasers is $12.80, find the cost of each. 19. Divide 36 into two parts in such a way that 1/5 of one part is equal to 1/7 of the other. 20. The length of the rectangle exceeds its breadth by 3 cm. If the length and breadth are each increased by 2 cm, then the area of new rectangle will be 70 sq. cm more than that of the given rectangle. Find the length and breadth of the given rectangle.

Answers for worksheet on word problems on linear equation in one variable are given below so that student can check the exact answers of the equation problems.

1. (a) x + 5 = 9

(b) x - 3 = 12

(c) 5x - 2 = 4

(d) 2(x + 7) = 13 2. 18, 30 3. 35 4. 12 5. 100 6. 18, 20 7. 15, 17, 19 8. 12, 18 years 9. 15 cm, 25 cm 10. 50 m, 100 m 11. 13/21 12. 15, 48 13. 30 girls, 12 boys 14. 72°, 108° 15. 16 years, 44 years 16. 50° 17. 11 years 18. eraser – 60 cents, pencil – 85 cents 19. 15, 21 20. length = 18 m, breadth = 15 m

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Worksheet on Linear Equations

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Linear Equations In Two Variables Worksheets

Linear equations in two variables worksheets can help encourage students to read and think about the questions, rather than simply recognizing a pattern to the solutions. linear equations in two variables worksheets come with the answer key and detailed solutions which the students can refer to anytime.

Benefits of Linear Equations in Two Variables Worksheets

Linear equations in two variables worksheets can help students to understand about the linear equation that it is an equation in which there are two variables used. the variable also can be used many times and/or can be used on either side of the equation; everything that matters is that the variable will remain the same.

Linear equations in two variables worksheets give students the opportunity to solve a wide variety of problems helping them to build a robust mathematical foundation. Linear equations in two variables worksheets help kids to improve their speed, accuracy, logical and reasoning skills in performing simple calculations related to the topic of linear equations in two variables.

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 linear equations.

Download Linear Equations in Two Variables Worksheet PDFs

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

Solving Equations Practice Questions

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Solving Linear Equations

In the video, students from a group are working on the card sort activity that is an early part of the lesson, where they are attempting to match the six story cards to expressions. While there were originally going to be two groups at this table, a student being absent means that they formed a larger group.

• Lesson Plan Intended Grade Level: Suggested Courses: Math 7
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