lesson 2 problem solving practice solve two step equations

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Two-Step Equation Worksheets

Two-step equation worksheets have a huge collection of printable practice pages to solve and verify the equations involving integers, fractions and decimals. Also, a number of exercise pdfs on translating two-step equations, MCQs and word problems based on geometric shapes are given here for additional practice for 7th grade and 8th grade students. Some of them are offered free of cost!

Solving Two-Step Equations involving Whole Numbers

Kick into gear solving single-variable two-step equations involving positive coefficients with this practice set! Rearrange the equations to make the variable the subject, and solve for its whole-number value.

• Download the set

Solving Equations involving Integers

In these worksheets solve the two-step equations with integer coefficients. Numerous worksheets are available for practice.

Solving Equations involving Fractions

Solve the equations which have fractions as their coefficients. Arrive the solution to the equations in just two steps.

Solving Equations involving Decimals

Decimal coefficients are included in these printable two-step equation worksheets. Solve these equations to get the value of the unknown.

Solving Equations: Mixed Review

Solve these mixed equations which involve fractions, integers and decimals. Each pdf two-step equation worksheet has ten problems for a thorough practice.

Equation Word Problems Worksheets

Utilize this set of worksheets to guide students of grade 7 and grade 8 to solve an array of diligently prepared equation word problems.

(15 Worksheets)

Solve and Verify the Solution

In these 12 worksheets solve each two-step equation to find the unknown. Substitute the value of the variable in the given equation to verify the solution.

Multiple Choice Questions

Identify the correct two-step equation or value from the given multiple responses. Each pdf worksheet has eight questions for practice.

Translating Two-Step Equation

In these printable worksheets, translate the given phrases and/ or sentences into two-step equation.

Find me! Solve these interesting problems following the given hints. Ex. If you add 7 to three times of me, you get 34. What number am I?

Equations in Geometry: Type 1

The lengths of the sides of geometric figures are given in the form of expressions. Use the given inputs to find the value of the unknown variables.

Equations in Geometry: Type 2

The properties of the geometric shapes are the clues to solve these word problems. Figure out the two-step equation from the given expressions to find the value of the unknown.

Related Worksheets

» One-step Equation

» Multi-step Equation

» Equation Word Problems

» Translating Phrases

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15 Awesome Activities To Learn Two-Step Equations

December 19, 2022 //  by  Narciss Greene

Are you teaching algebra? If it takes more than one step to solve for “X”, you are likely focusing on two-step equations! Even though multi-step equations may be tricky for some learners, that does not mean they can’t be interesting. All you need is some encouraging collaboration and new activities to add a fun spin to your next lesson. Whether you’re looking for a simple math review game or a way to collect real-time student data, this list has you covered.

1. Worksheet Relay Race

This 2-step equations partner activity makes for some great extra practice right before test day. Print out two of these worksheets and have students form two lines. One student solves the first question and passes the paper to the next student. Whichever line finishes first with 100% accuracy wins!

Learn More: Math Worksheets 4 Kids

2. Jigsaw a Worksheet

This worksheet, with student answers included, has five-word problems. Break students up into five teams and have them work together to solve their assigned problem. Once finished, have a volunteer from each group teach their answer to the class. 

3. Cut and Paste

Once students solve the problems, they cut them out and place them in the appropriate spot. At the end of this independent practice, they will have spelled a secret message. This is one of those equation activities that double as a self-checking scavenger hunt!

Learn More: Common Core Material

4. Stained Glass

Color-coded coloring, making straight lines, and math all in one! Once students solve a 2-step equation, they will use a ruler to connect the answer to the letter associated with that letter. The best part is students know immediately if they arrived at the correct answer or not.

Learn More: Math in Demand

5. Online Quiz Game

This link provides a full lesson plan for 8-step equations. First, watch a video and discuss. Then learn the vocabulary, do a little reading, practice some word and number problems, and end with the online quiz game. 

Learn More: Generation Genius

6. Take a Trip

Help Tyler’s family with their sightseeing tour of Philadelphia. The real-world scenarios in this math activity provide a fun approach to learning two-step equations. This adventure activity will take students through Tyler’s vacation by helping him get to his destination safely.

Learn More: Education

7. Around the Room

Cut each of these out and have students solve them as they walk around the room. It will add to your classroom décor and give the students an opportunity to get out of their seats. Having sets of boards that students can write on as they move around your math classroom will be helpful here.

8. Make a Flowchart

In the midst of the variety of activities available, sometimes simply taking notes can help cement new ideas. Virtual manipulatives could work here, or just plain paper. Provide students with colored paper and markers to spruce up their flowcharts. Please encourage them to keep these notes out for future algebra activities.

Learn More: Cue Math

9. Venn Diagram

The link below walks students through what a two-step equation is, how to solve them, and answers the questions at the end. It then goes into the difference between one and two-step equations. Use this link as an activity for subs and have students turn in their Venn Diagrams of the difference between one and two-step equations by the end of class.

10. Play Hangman

Students work through solving these equations to figure out what six-letter word is at the top of this practice worksheet. If one of their answers matches the inequality under the blank line, they will use the letter from the box they just solved to start spelling the word. If they solve a box that does not have an answer at the top, the hangman starts appearing. 

Learn More: The Best of Teacher Entrepreneurs

11. Play Kahoot

Check out the series of questions in any digital review activity found here. Kahoot provides an easy self-checking activity with little competition. Get a bunch of friends together to complete this activity in class. The student who answers accurately and quickly will win!

Learn More: Kahoot

12. Play Battleship

Yay for math ship activities! Your students will need to know about positive integers and negative integers to engage in this virtual activity. Each time they solve a 2-step equation in this independent activity, they work closer to sinking their enemies. This fun activity is sure to make for a funny story at dinnertime!

Learn More: Quia

13. Shoot Hoops

This fun partner activity has a red team and a blue team. Bring on the competition, engagement level, and skill-building with this in-class practice! Each time they answer the question correctly, their team scores a point in the game. 

Learn More: Math-Play

14. Word Wall Match Up

While this can be one of those perfect pre-made digital activities to have in your back pocket, it would also be great for cutting out for your next mix-match activity. I would get rid of the digital component and make this a hands-on activity where students partner up to match the equation to the words.

Learn More from this resource library: Word Wall

15. Play Bingo

After spinning the wheel, you can either resume playing or eliminate that section of the wheel with this two-step equation activity. You’ll need to print out a Bingo form for students ahead of time. As the wheel spins, students will mark off that answer on their Bingo cards. 

Learn More: Word Wall

GED Math Books designed especially for struggling students

Solving Two-Step Equations

Order Matters

What does the order of operations have to do with solving equations? Quite a bit, as it turns out. In this lesson, Kate uses the order of operations to explain why we solve two-step equations the way we do. 

STEP 1: WATCH THE VIRTUAL CLASS VIDEO AND TAKE NOTES

Make sure to note the following:.

Simplifying and solving are opposite procedures. Because of this, you actually work the order of operations BACKWARDS when solving equations. 

Ask a Question

Do you have a question about the class video, practice, or example problems? Post a picture to our FB group for immediate assistance. Be sure to include the lesson name and level in your post. 

STEP 2: COMPLETE ONE LEVEL OF PRACTICE

Solve two-step equations involving whole numbers and the basic operations.

EXPERIENCED

This worksheet from Kuta Software has you solve two step equations with negatives. 

Mixed practice with negatives, fractions, and exponents. 

NEED MORE HELP? CHECK OUT THE EXAMPLE VIDEOS 

Beginner Solution Playlist

Experienced Solution Playlist

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Two-Step Equations

Solving two-step equations.

There is no doubt that solving a two-step equation is extremely easy. As the name implies, two-step equations can be solved in just two steps. If this is your first encounter with two-step equations, don’t worry because we will go over enough examples to make you familiar with the process.

When solving an equation in general, we always keep in mind the notion that whatever we do to one side of the equation should also be done to the other side to ensure that the equation remains balanced.

We know that we have completely solved a two-step equation if the variable, usually represented by a letter in an alphabet, is isolated on one side of the equation (either left or right) and the number is located on the opposite side.

The USUAL way of solving a two-step equation:

Note : This is the “usual” method because most of the two-step equations are solved this way. Notice that Step 2 can alternatively be replaced by Step 3 which are the same essentially.

1)  First, add or subtract both sides of the linear equation by the same number.

2)  Secondly, multiply or divide both sides of the linear equation by the same number.

3)* Instead of step #2, always multiply both sides of the equation by the reciprocal of the coefficient of the variable.

Examples of How to Solve Two-Step Equations

Example 1: Solve the two-step equation below.

As the name of this linear equation suggests, it requires two steps in order to solve for the unknown variable. Generally, the first step involves getting rid of the number “farthest” from the term with a variable being solved. Then, we eliminate the number “closest” to the variable. The number is either multiplying or dividing the variable. It is also called the coefficient of the term.

The variable here is [latex]x[/latex]. Our goal is to solve [latex]x[/latex] by isolating it on one side of the equation. Keeping the variable on the left or on the right doesn’t make any difference. It is up to you! In this problem, let’s keep it on the left side since it’s already there.

On the side (left side of the linear equation) where the variable is located, notice that [latex]2[/latex] is “closest” to variable [latex]x[/latex], and [latex]5[/latex] is “farthest” one.

This simple observation allows us to decide which number to eliminate first. It is obviously [latex]+5[/latex] because it is farther between the two. The opposite of [latex]+5[/latex] is [latex]-5[/latex], that means we will subtract both sides of the equation by [latex]5[/latex].

After eliminating [latex]5[/latex] on the left side of the equation by subtracting both sides by [latex]5[/latex], it’s time to get rid of the number closest or directly attached to [latex]x[/latex] which is [latex]2[/latex] in [latex]2x[/latex]. Since [latex]2[/latex] is multiplying the variable [latex]x[/latex], its opposite operation is to divide by [latex]2[/latex].

After dividing both sides by [latex]2[/latex], we obtain the final answer or solution to the given two-step linear equation.

Just a quick reminder, it is considered solved because the coefficient of the variable is just  positive one, [latex]+1[/latex].

Example 2: Solve the two-step equation below.

Our goal is to keep the variable [latex]x[/latex] on one side of the equation. It doesn’t matter which side, however it is a “standard” practice to keep the variable being solved to the left side. Some algebra teachers may require you to keep the variable to the left and there’s nothing with that. Personally, I don’t mind where you keep the variable, either left or right, as long as the isolated variable on one side of the equation has a coefficient of [latex]+1[/latex].

The first step involves removing the number “farthest” from variable [latex]x[/latex]. Notice that [latex]-3[/latex] is “closest” to [latex]x[/latex], while [latex]-8[/latex] is “farther away”. So then, we can eliminate [latex]-8[/latex] by adding to its opposite which is [latex]+8[/latex].

The second step involves getting rid of the number closest to the variable [latex]x[/latex] which is [latex]-3[/latex]. Since [latex]-3[/latex] is multiplying the variable x, its opposite operation is to divide by [latex]-3[/latex]. After dividing both sides by [latex]-3[/latex], we have solved the linear equation.

Quick reminder, [latex]-3[/latex] divided by [latex]-3[/latex] is equal to [latex]+1[/latex].

Example 3: Solve the two-step equation below.

Here’s a situation where we can isolate the variable [latex]x[/latex] to the right side of the equation since it is already there.

Looking at the right side of the equation where the variable is located, the number [latex]3[/latex] is closest to [latex]x[/latex] because [latex]3[/latex] is dividing the variable [latex]x[/latex]. On the other hand, the number [latex]26[/latex] is “farther away”. This implies that we will have to deal with [latex]+26[/latex] by subtracting both sides of the equation by [latex]26[/latex]. The reason we subtract is that the additive inverse of [latex]+26[/latex] is [latex]-26[/latex].

The second step is to get rid of the denominator [latex]3[/latex]. Since [latex]3[/latex] is dividing the [latex]x[/latex], its opposite operation is to multiply by [latex]3[/latex].

After multiplying both sides by [latex]3[/latex], we have arrived at the final answer. You may rewrite your final answer as [latex]x = -9[/latex].

Example 4: Solve the two-equation below.

This may appear to be a multi-step equation, but it is not. It can be solved in two steps. Don’t be bothered by the fractions because they are very easy to deal with. In this case, you will apply the rule of fraction addition. The rule states that if you are adding two fractions that have the same denominator, just add the numerators then copy the common denominator.

Back to solving the two-step equation above, to remove the fraction on the left side which is [latex]\Large{ – {3 \over {10}}}[/latex], we will add [latex]\Large{{3 \over {10}}}[/latex] to both sides of the equation.

The reason that we are adding instead of subtracting is because the additive inverse of [latex]\Large{ – {3 \over {10}}}[/latex] is [latex]\Large{+ {3 \over {10}}}[/latex]  .

After adding [latex]\Large{{3 \over {10}}}[/latex] to both sides, only [latex]{\Large{{2 \over 5}}}x[/latex] remains on the left side.

For the right side of the equation, we have [latex]\Large{{9 \over {10}} + {3 \over {10}} = {{12} \over {10}}}[/latex].

Everything I stated above is just the first step. Now, moving on to the second step. Look at the coefficient of the variable [latex]x[/latex]. It is [latex]\Large{{2 \over 5}}[/latex] that means its reciprocal is [latex]\Large{{5 \over 2}}[/latex].

To finally solve the given equation, we will multiply both sides of the equation by the reciprocal of the coefficient of the variable in question. Here’s the complete step-by-step solution:

Take a quiz:

• Two-Step Equations Quiz

You might also like these tutorials:

• Two-Step Equations Practice Problems with Answers
• Multi-Step Equations Practice Problems with Answers

Solving Two-Step Equations

In these lessons, we will look at solving equations that require two steps.

Related Pages Solving Equations Algebraic Expressions More Algebra Lessons

The following figure shows how to solve two-step equations. Scroll down the page for more examples and solutions.

In order to solve two-step equations, we need to work backwards with regards to the order of operations. We would perform the addition & subtraction before multiplication & division.

• Add or subtract to isolate the variable term.
• Multiply or divide to solve for the variable.
• Check your solutions.

Example: Solve 3x – 2 = 16

Solution: In the equation 3x – 2 = 16, notice that the variable is being multiplied and has a term being subtracted. To isolate the variable, we need to add 2 to both sides and then divide both sides by 3.

3x – 2 = 16 3x – 2 + 2 = 16 + 2 (add 2 to both sides) 3x = 18 (simplify) x = 6 (divide both sides by 3)

Check: 3x – 2 = 16 3 • 6 – 2 = 16 (Substitute x = 6 into the original equation)

How To Solve Basic Two Step Equations?

Examples: a) 2x + 3 = 9 b) 5x – 8 = 22 c) 9 – 2x = 23 d) –11 = 4x – 43 e) –15 = 5 – 5x

How To Solve Two Step Linear Equations With Fractions?

In this video, the equations are solve by working with the fraction, not be clearing the fractions from the equation.

• 2x + 1/4 = 3/5
• 2/5 x - 1/2 = 3/5
• 1/4 = 3/5 x - 5
• 2 1/5 = 2/3 - 1/2 x

How To Solve Two Step Linear Equations Involving Decimals?

• 0.3x - 2.16 = 9.9
• x/2.1 + 4.93 = 10.45

How To Solve The Different Types Of Two Step Equations?

• 2x + 3 = 25
• x/4 - 2 = -5
• 4 - 2x = 10
• 4 = 6 - x/3
• 4.3 = 1.5x - 5
• x/3 - 3/4 = 1/6

Examples Of Solving Two-Step Equations

• b/3 + 13 = 11
• 9g + 11 = 2
• t/4 - 10 = -6
• 15x + 3 = 48

How To Solve A Two-Step Equation? (undo PEMDAS in reverse to solve)

Example: 4x + 8 = 24

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is as straightforward as it sounds. You will need to perform two steps in order to solve the equation. One goal in solving an is to have only variables on one of the equal sign and numbers on the other of the equal sign. The other goal is to have the number in front of the equal to one. The does not always have to be x. These equations can make use of any letter as a variable. The strategy for getting the by itself with a of 1 involves using opposite operations. For example, to move something that is added to the other of the equation, you should subtract. The most important thing to remember in solving a is that whatever you do to one of the equation, you MUST do to the other side. So if you subtract a number from one side, you MUST subtract the same value from the other side. You will see how this works in the examples. In solving two-step equations you will make use of the same techniques used in solving only you will perform two operations rather than just one. by itself on one side. We need to get rid of the 4 that is added, so we’ll need to subtract 4 from both sides. Even after doing that, there is still a 3 multiplied by the variable, so division will be necessary to eliminate it. is not by itself on one side. We will get rid of the 5 that is added by subtracting 5 from both sides. This still leaves a -2 in front of the so we will have to divide both sides by -2. is not by itself on one side. We will need to get rid of the -5 by adding 5 to both side. We will then need to multiply both sides by the of To get help solving more complicated equations, click here (link to one var multi step.doc)
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Two Step Equations Worksheets

Equation Skills

Math Mysteries

Safe Solver

Equation Quest

Algebra Action

Fraction Fusion

Decimal Dives

Fraction Fixers

Fraction Focus

Solve Safari

App Adventure

Equation Expedition

Variable Voyage

Fraction Frenzy

Equation Explorers

About these 15 worksheets.

This collection of worksheets can help students grasp the fundamental concepts of solving algebraic equations that require two operations to find the solution. These worksheets provide structured practice, guiding students through the necessary steps to isolate a variable and solve for its value. In doing so, they not only reinforce the algebraic operations but also develop critical thinking and problem-solving skills that are vital for more advanced math topics.

These types of worksheets commonly focuses on a series of equations where students need to perform two distinct operations to solve for the variable. The operations usually involve a combination of addition, subtraction, multiplication, and division. The goal is for students to learn the process of isolating the variable by systematically undoing these operations, starting with the operation that is furthest from the variable. For instance, if a student is given an equation like 7x + 16 = 65, the worksheet will guide them to first subtract 16 from both sides, and then divide by 7 to find the value of x. This step-by-step method ensures that students understand the inverse operations needed to solve the equation, fostering a deeper understanding of algebraic principles.

Beyond the basic equations, some worksheets include variations that present equations with different complexities, such as involving fractions or negative numbers. These variations challenge students to apply the same principles in slightly more complex scenarios. For example, a problem like 3a/4 = 6 requires students to first multiply both sides by 4 and then divide by 3 to solve for a. This introduces students to working with fractions within the context of algebra, reinforcing their understanding of how to manipulate and solve equations that aren’t just simple whole numbers.

Another common type of Two Step Equations worksheet introduces word problems, where students must translate a real-world scenario into an algebraic equation and then solve it. This type of problem is particularly valuable because it teaches students to connect abstract mathematical concepts with practical applications. For example, a word problem might state, “When 13 is added to twice the value of a given number, the value obtained is 85. Find the number.” Here, students must first interpret the problem to create the equation 2x + 13 = 85 and then solve for x. By doing this, students not only practice their algebra skills but also learn how to apply these skills in everyday situations, which is a crucial aspect of mathematics education.

Some of the worksheets focus on more intricate aspects of solving two-step equations, such as dealing with negative numbers, decimals, or variables on both sides of the equation. These types of problems prepare students for more advanced algebra by introducing them to the idea that equations can exist in various forms and require a flexible approach to solve. For example, a problem like 8x – 3 = 53 first requires the student to add 3 to both sides and then divide by 8. This not only reinforces the basic operations but also introduces the idea that equations can involve subtraction or addition of variables and constants, which is a stepping stone to more complex algebraic manipulations.

The progression from simple to more complex equations in these worksheets is intentional and well-designed. It ensures that students build a solid foundation in basic algebra before moving on to more challenging problems. By starting with straightforward equations, students gain confidence in their ability to manipulate and solve equations. As they progress, they encounter problems that gradually increase in complexity, introducing new concepts and techniques in a manageable way.

These worksheets include problems that require students to show their work step-by-step. This not only helps teachers assess the students’ understanding but also encourages students to develop a disciplined approach to solving equations. By writing down each step, students can track their thought process, catch mistakes, and better understand the logic behind each operation. This methodical approach is crucial for success in algebra and other areas of mathematics.

How To Solve Two Step Equations

Solve the equation – 3x + 7 = 16

Step #1 – Identify the Equation and Goal

The equation given as – 3x + 7 = 16

Our goal is to isolate x, which means we want to get x by itself on one side of the equation. This will help us identify the numeric value that x represents.

Step #2 – Eliminate the Constant Term

The first operation we need to undo is the addition of 7 to the term with x.

To eliminate the +7, subtract 7 from both sides of the equation.

3x + 7 – 7 = 16 – 7

Simplifying both sides gives us – 3x = 9

Step #3 – Eliminate the coefficient of the variable

Now, the equation is 3x = 9. The next step is to eliminate the coefficient of x, which is 3.

To isolate x, divide both sides of the equation by 3:

Simplifying both sides gives us – x = 3

Two-Step Equations

Two step equations are equations that can be solved within exactly two steps. Two step equations are extremely easy to solve. As the name suggests, two step equations take only two steps to solve. These equations are just a little complicated than the one step equations. While solving a two step equation, we need to perform the operation on both sides of the equals to sign.

In this article, we will understand the meaning of two step equations with integers, decimals, and fractions, how to solve them, the golden rule to solve two step equations along with some examples for a better understanding.

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What are Two Step Equations?

Two step equations are algebraic problems that take just two steps to solve. The two step equation is a linear equation in one variable . While performing an operation for solving a two step equation, we need to perform the same operation on both sides of the equation. We isolate the variable on one side of the equation to determine its value.

Two Step Equations Definition

Two step equations are algebraic equations and are the equations that can be solved in exactly two steps and gives the final value of the variable in two steps. Generally, two step equations are of the form ax + b = c, where a, b, c are real numbers. A few examples of two step equations are:

• 0.3y + 5 = 1
• (2/3)z - 12 = 10

Solving Two Step Equations

Two step equations are very easy to solve. It includes just one extra step as compared to one-step equations to solve. We can solve a two-step equation by isolating the variable (usually represented by an alphabet or letter) on one side of the equation and all other values on the other side. The general two steps to solve the two-step equations are:

• Step 1: Addition and subtraction to isolate the variable.
• Step 2: Multiplication  or division  to determine the value of the variable.

Let us consider a few examples and solve two-step equations to understand the concept of solving two-step equations.

Example 1: Solve the equation 2x + 6 = 12.

To solve the two step equation 2x + 6 = 12, we need to determine the value of x. Let us solve it step-wise.

Step 1: Subtract -6 from both sides of the equation to isolate the variable x.

2x + 6 - 6 = 12 - 6

Step 2: Divide both sides of the equation by 2 to solve for x.

Hence, we have solved the equation 2x + 3 = 12 in just two steps.

Thus the two-step equation can be easily solved in a sequence of steps, as presented above.

Two-Step Equations with Decimals and Fractions

Two step equations that have decimals and fractions as the coefficient of the variable and constant term are said to be two step equations with decimals and fractions. A few examples of two step equations with fractions and decimals are:

• 0.3 x + 2/3 = 1
• 3x - 0.5 = 1.2
• (1/3) x + 4/5 = 3/4

These equations are solved in the same manner as the general two steps equations and the same steps are followed to determine the value of the variable.

Golden Rule to Solve Two Step Equations

The golden rule to solve two step equations is to perform all operations simultaneously on both sides of the equation. To isolate the variable on one side of the equation and to determine its value, we first add or subtract on both sides of the equation and then multiply or divide on both sides to get the final solution of the two step equation.

Important Notes on Two Step Equations

• Remove the parentheses and combine like terms to simplify each side of the two-step equation.
• Always remove the constant first by adding or subtracting the appropriate number.
• Always verify the solution in the end.

Topics Related to Two Step Equations

• Equations in Math
• Simple equations
• Algebraic formulas

Two Step Equations Examples

Example 1: Solve the two step equation (x/6) - 7 = 11

Solution: To solve the given two step equation, we will follow the steps discussed above in the article.

Step 1: Add 7 to both sides of the given two step equation

(x/6) - 7 + 7 = 11 + 7

⇒ (x/6) = 18

Step 2: Multiply both sides of the equation by 6.

6 × x/6 = 6 × 18

Answer: Hence the solution to the given two step equation (x/6) - 7 = 11 is x = 108.

Example 2: Determine the solution of the two step equation (2/3) z + 0.8 = 1.5

Step 1: Subtract 0.8 from both sides of the given two step equation

(2/3) z + 0.8 - 0.8 = 1.5 - 0.8

⇒ (2/3) z = 0.7

Step 2: Multiply both sides of the equation by (3/2).

(3/2) × (2/3) z = (3/2) × 0.7

Answer: Hence the solution to the given two step equation (2/3) z + 0.8 = 1.5 is x = 1.05

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Practice Questions on Two Step Equations

Faqs on two step equations, what are two step equations in algebra.

Two step equations are algebraic equations that take just two steps to solve.First, the variable is isolated by adding or subtracting a numeric value on both sides of the equation. Secondly, the value of the variable is computed by multiplying or dividing the variable by an appropriate number.

What are the Steps to Solve Two Step Equations?

The general two steps to solve two step equations are:

• Step 1: Simplify the given equation by removing all brackets and parenthesis:
• Step 2: Add or subtract to isolate the variable.
• Step 2: Multiply or divide to determine the value of the variable.
• Step: Verify the answer by substituting it in the given equation .

How to Solve Two Step Equations?

Two step equations can be solved by following two quick steps:

• Step 1: Add or subtract numbers on either sides, to isolate the variable.

IS Two Step Equation the Same as A Multi-Step Equation?

Two-step equation can also be called a multi-step equation since it involves more than one step. And a multi-step equation can have two or more steps, in the process of solving the equation.

What is the Difference Between One Step and Two Step Equations?

One step equations take just one step to solve whereas two steps equations take two steps to get to the solution. Two-step equations include just one extra step as compared to one step equations to solve.

What is the Goal of Solving Two Step Equations?

The goal of solving two step equations is to isolate the variable and determine the value of the variable. And in the end, the variable should satisfy the given two step equation.

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Solve Two-Step Equations #3

Give students even more practice solving two-step equations with this helpful practice worksheet! Designed for seventh- and eighth-grade math students, this worksheet is a great way to provide learners independent practice as they solve two-step, one-variable equations containing integer coefficients and constants. Mastering this algebra skill will prepare students for the next step of solving multi-step equations. For extra practice, try Solve Two-Step Equations #1 and Solve Two-Step Equations #2 .

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Chapter 3, Lesson 5: Solving Two-Step Equations

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Two-step Equations – Definition, Steps, Facts, Examples, FAQs

What are two-step equations, how to solve two-step equations, what are the rules to solve two-step equations, solved examples on two-step equations, practice problems on two-step equations, frequently asked questions on two-step equations.

Two-step equations are mathematical equations that require only two steps to solve and find the value of the variable. In order to solve two step equations, we need to undo two operations.

Two-step equation example:

	$4x\;-\;1 = 15$
	Undo the subtraction operation. 4x – 1 + 1 = 15 + 1 4x = 16
	Undo the multiplication operation. $\frac{4x}{4} = \frac{16}{4}$ x = 4

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Two-Step Equations: Definition

Two-step equations are algebraic equations that can be solved in two steps.

Two step equations may come in different forms involving combinations of addition , subtraction , multiplication , or division operation.

Examples of two-step equations:

• $2x + 1 = 5$
• $\frac{7x}{\;-\;2} = 21$

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When solving two-step algebraic equations, the goal is to isolate the variable on one side of the equation. 

To isolate the variable, we have to undo the involved operations by using their inverse operations (opposite operations) and solve for the varibale. 

Addition (+)	Subtraction (-)
Subtraction  (-)	Addition (+)
Multiplication ($\times$)	Division ($\div$)
Division ($\div$)	Multiplication ($\times$)

In most of the two-step equations, usually we first use addition or subtraction operation to isolate the variable and in the second step, we use multiplication or division to find the value of the variable.

Example: Solve $2x + 1 = 5$

Subtract 1 from both sides.

$2x + 1\;-\;1 = 5\;-\;1$

Divide both sides by 2.

$\frac{2x}{2} = \frac{4}{2}$

$x = 2$                        

To solve two step equation, we need to balance both sides of the equation using following rules: 

• Undo the addition by subtracting both sides with the same number.
• Undo subtraction by adding both sides with the same number.
• Undo the multiplication by dividing both sides with the same number.
• Undo the division by multiplying the same number to both sides. 

Facts about Two-step Equations

• Solving two-step equations helps build the foundation for solving multi-step algebraic equations.
• The first step in solving a two-step equation is usually undoing addition or subtraction by applying the inverse operation.
• The second step generally involves undoing multiplication or division by applying the inverse operation.

Conclusion 

Two-step equation has one variable and two mathematical operations in it. Using the order of operations in reverse we can reach the solution by finding the value of an unknown variable. Even though we can use different methods to solve this two step equation, solving through reverse order of operations is the easiest way.

Example 1: Solve 3x + 12 = 21.

Solution:  

 3x + 12 = 21

Undo the addition operation by subtracting 12 from both sides of the equation. 

3x + 12 – 12 = 21 – 12 

3x + 0 = 9 

Undo the multiplication operation by dividing both sides of the equation by 3 we get,

$\frac{3}{3} x = \frac{9}{3}$

 x = 3

Example 2: Sam sold one-fourth of his watch collection, and then sold 5 more watches. How many watches did Sam have in the beginning if he sold a total of 10 watches?  

Solution: 

Suppose that Sam had x number of watches initially in his collection.

First, he sold one-fourth of his collection, which is $\frac{x}{4}$. 

Next, he sold 5 more watches.

So, total number of watched he sold $= \frac{x}{4} + 5$

It is given that Sam sold a total of 10 watches.

Thus,  $\frac{x}{4} + 5 = 10$

Undo the subtraction by adding the number 5 on both sides of the equation we get, 

$\frac{x}{4} + 5 \;-\; 5 = 10 \;-\; 5$

$\frac{x}{4} = 5$

Undo the division operation by multiplying number 4 on both sides of the equation we get, 

$\frac{4x}{4} = 5 \times 4$

Hence, Ramsey had 20 watches with him in the beginning. 

Example 3: Solve 2 (x + 7) = 16 .

2 (x + 7) = 16

$\frac{2}{2} (x + 7) = \frac{16}{2}$ divide by 2 on both sides

x + 7 – 7 = 8 – 7 subtract 7 from both sides 

x = 1                                                                                                                                                                                 

Another way: If we expand this equation, we get

 2x + 14 = 16

2x = 16 – 14

Example 4: Solve the two step equation $\frac{x \;-\; 2}{3} = 1$

$\frac{x \;-\; 2}{3} = 1$ 

$\frac{3(x \;-\; 2)}{3} = 1 \times 3$ multiplying 3 on both sides of the equation we get,                                                

x – 2 = 3 adding 2 on both sides of the equation we get, 

x – 2 + 2  = 3 + 2 

Two-step Equations - Definition, Steps, Facts, Examples, FAQs

Attend this quiz & Test your knowledge.

Find the value of x if 2x+3=5.

Solve: - x + 1 = 12, what are two-step equations.

What is a multi-step equation?

A multi-step equation contains mixed operations such as addition, subtraction, multiplication, or division. It requires two or more steps to solve the equation. We can use the reverse order of operations to solve them.

What are one-step equations?

One-step equations are algebraic equations that require only one step to solve.

How do you check if the solution to a two-step equation is correct?

To check the solution, substitute the found value back into the original equation and verify if both sides are equal.

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Reviewing two-step equations in 7th or 8th grade? These print and digital partner worksheets are a fun spin on the classic game of Battleship! Students review 2-step equations involving addition, subtraction, division, and multiplication as they take turns attacking spaces and sinking ships. This two-step equations game will have your students begging for more activities just like it!

No prep – simply print or share digitally for an instant, interactive learning experience. This dynamic two-step equations review game goes beyond reinforcing essential math skills – it keeps your students eagerly engaged in meaningful practice. Elevate your lesson and make learning enjoyable with this innovative resource!

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