Two Step Equations Worksheet Library

Download Free Solving Two Step Equations Worksheets with Answer Keys

Free Solving Two Step Equations Worksheets (with Answers)

Are you looking for free two step equations practice worksheets to give yourself or students some extra practice with this key algebra skill?

If so, welcome to our Two Step Equations Worksheet Library, where you can download several free PDF practice worksheets. Each solving two step equations worksheet is available to download as a printable PDF file with practice problems on the first page and a complete answer key on page two.

You can download any of our two-step equations worksheets by clicking on the blue text links shared in the library below. When you click on a text link, a preview window will appear where you will have the option to save and/or print the corresponding PDF worksheet.

This page also includes a review section that includes a step-by-step tutorial of how to solve two-step algebraic equations, including several example problems and how to solve them.

Each solving two step equations worksheet in the library below is a sample activity from the Mashup Math K-12 Worksheet Libraries available on our website, where you can download hundreds of free practice worksheets. | Quick Links: How to Download/Print

Two Step Equations Worksheet Library

Two Step Equations Worksheet (A)

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Two Step Equations Worksheet (B)

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Two Step Equations Worksheet (C)

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Two Step Equations Worksheet Review

If you are having trouble with solving problems on any solving two step equations worksheet in the library above, then we strongly recommend that you read through this review and work through the practice problems to make sure that you have a solid understanding of how to solve two step algebraic equations.

The key to solving two-step algebraic equations is having a strong understanding of inverse operations, namely that:

  • The opposite of addition is subtraction and vice versa.

  • The opposite of multiplication is division and vice versa.

Whenever you have to solve a two-step equation (or any algebraic equation), the goal is always to isolate the variable (i.e. the goal is to get the variable all by itself on one side of the equals sign).

Now, let’s work through a few examples of how to solve a two-step equations.

Solving Two-Step Equations Example #1

Example: Solve for x: 4x - 6 = 18

Remember that our goal is to use inverse operations to rearrange the equation, 4x - 6 = 18, so that the variable, x, is isolated on one side of the equals sign. And, since this is a two-step algebraic equation, we should be able to achieve our goal of getting x by itself in two steps, as follows:

  • Step One: Isolate the x-term

  • 4x - 6 = 18

  • 4x - 6 (+6) = 18 (+6)

  • 4x = 24

To complete the first step, we want to move the -6 from the left side of the equation to the right side (thus isolating the 4x term). We can do that by performing inverse operations and adding 6 to each side. On the left side, -6 and 6 cancel each other out. On the right side, 18 +6 equals 24, and we are left with 4x = 24. Now we are ready for our second and final step:

  • Step Two: Solve for x

  • 4x =24

  • (4x)/4 = (24)/4

  • x = 6

For the next step, we just have to divide both sides of the equation by 4 to isolate the variable, x. The result is that x=6.

Final Answer: x=6 is the solution to the two-step equation 4x - 6 = 18.

How can we check our answer? Take your answer, x=6, and substitute it into the original equation, 4x - 6 = 18, and check if the equation works out:

  • 4x - 6 = 18

  • 4(6) - 6 = 18

  • 24 -6 = 18

  • 18 = 18 ✔

Our answer checks out and we have solved the equation! Figure 01 below illustrates our step-by-step process for solving this example.

 

Figure 01: Two Step Equations Worksheet Review: Example #1 Solved

 

Solving Two-Step Equations Example #2

Example: Solve for x: 2 + x/6 = -10

Just like the previous example, our goal for solving this algebraic equation is to use inverse operations to get the variable, x, by itself.

And we can again use the same two steps from the previous example to achieve that goal as follows:

  • Step One: Isolate the x-term

  • 2 + x/6 = -10

  • 2 -2 + x/6 = -10 -2

  • x/6 = -12

For our first step, we want to get the x-term (x/6) isolated, and we can do that by moving the 2 from the left side of the equation to the right side of the equation. This can be achieved by performing inverse operations (i.e. subtracting 2 from both sides of the equation), which results in x/6 = -12.

  • Step Two: Solve for x

  • x/6 = -12

  • 6(x/6) = 6(-12)

  • x = -72

For the second step, we just had to multiply both sides by 6 to isolate the variable, x. The result is that x=-72.

Final Answer: x=-72 is the solution to the two-step equation 2 + x/6 = -10

Finally, we can check our answer by substituting x=-72 it into the original to see if it works out or not. If we get the same result on both sides of the equals sign, then we know that we have solved the problem correctly. If we do not, then we should go back and work through the problem again, looking for any possible mistakes.

  • 2 + x/6 = -10

  • 2 + (-72)/6 = -10

  • 2 + -12 = -10

  • -10= -10 ✔

Since our result is -10 on both sides, our answer checks out and we have successfully solved this two-step equation! The entire step-by-step process to solving this second example is shown in Figure 02 below.

 

Figure 02: Solving Two Step Equations Worksheet Review: Example #2

 

After completing these two examples, it should be easier to see that the process to solving two step equations is relatively straightforward. Just be sure that you always remember the following key tips:

  • The goal of solving any algebraic equation, including two-step equations, is to isolate the variable (i.e. get the variable by itself).

  • You can rearrange terms of an equation from one side of the equals sign to the other by using inverse operations.

  • Addition is the inverse of subtraction and vice versa, and multiplication is the inverse of addition and vice versa.

  • Always check your final answer by substituting it back into the original equation to see if the result of the left side of the equals sign is the same value as the result of the right side.