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Grade 7 Math Worksheets

There are three sets of solving equation worksheets:

- Solve 1-step equations
- Solve 2-step equations
- Solve Proportion Equations
- Solve Absolute Value Equations

Examples, solutions, videos, and worksheets to help Grade 7 and Grade 8 students learn how to solve absolute equations.

There are four sets of simplifying algebraic expression worksheets.

- Absolute Value Equations (1-step)
- Absolute Value Equations (2-step)
- Absolute Value Equations (1-step with fractions)
- Absolute Value Equations (fractional expressions)

To solve absolute value equations, you need to consider two cases: one where the expression inside the absolute value is positive and one where it is negative. Here’s a step-by-step guide on how to solve absolute value equations:

- Write the absolute value equation in the form |expression| = constant.
- Set up two separate equations, one with the expression inside the absolute value as positive and one with it as negative.
- Solve both equations for the variable.
- Check your solutions to ensure they satisfy the original absolute value equation.

Let’s go through an example to illustrate the steps:

Example: Solve the absolute value equation |2x - 5| - 13 = -6.

- Write the absolute value equation in the required form:

|2x - 5| = 7 - Set up two separate equations:

Case 1: 2x - 5 = 7

Case 2: 2x - 5 = -7 - Solve both equations:

Case 1: 2x - 5 = 7

x = 6

Case 2: 2x - 5 = -7

Subtract 5 from both sides:

x = -1 - Check the solutions:

Substitute x = 6 into the original equation:

|2(6) - 5| - 13 = |12 - 5| - 13 = |7| - 13 = -6 (True)

Substitute x = -1 into the original equation:

|2(-1) - 5| - 13 = |-2 - 5| - 13 = |-7| - 13 = -6 (True)

Both solutions, x = 6 and x = -1, satisfy the original absolute value equation |2x - 5| - 13 = -6.

So, the solutions to the absolute value equation are x = 6 and x = -1.

The following diagram shows another example of solving an absolute value equation.

Have a look at this video if you need to review how to solve absolute value equations.

Click on the following worksheet to get a printable pdf document.

Scroll down the page for more **Absolute Value Equation Worksheets**.

**Printable**

(Answers on the second page.)

Absolute Value Equation Worksheet #1 (1-step)

Absolute Value Equation Worksheet #2 (2-step)

Absolute Value Equation Worksheet #3 (1-step with fractions)

Absolute Value Equation Worksheet #4 (fractional expressions)

**Online or Generated**

1-step Equations (Add or Subtract)

1-step Equations (Multiply or Divide)

Solving 1-Step Equations

2-Step Equations

Solving 2-Step Equations

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

Solve Absolute Value Equations

Solving Equations by Combining like terms

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