Absolute Value Equation Worksheets

There are four 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 equations that involve absolute values.

How to solve absolute value equations?

There are ten sets of solving absolute value equations worksheets.

• Absolute Value Equations (1-step)
• Absolute Value Equations (2-step)
• Absolute Value Equations (1-step with fractions)
• Absolute Value Equations (fractional expressions)
• Type of Equations: |-3x|= 9
• Type of Equations: |y + 4| = 21
• Type of Equations: |3t - 5| = 15
• Type of Equations: |\( \frac{4}{5} \)b| = 32
• Type of Equations: \( \frac{|c + 3|}{4} \)= 12
• Type of Equations: |\( \frac{d}{7} \) + 10| = 28

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:

1. Write the absolute value equation in the form |expression| = constant.
2. Set up two separate equations, one with the expression inside the absolute value as positive and one with it as negative.
3. Solve both equations for the variable.
4. 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.

1. Write the absolute value equation in the required form:
   |2x - 5| = 7
2. Set up two separate equations:
   Case 1: 2x - 5 = 7
   Case 2: 2x - 5 = -7
   
3. Solve both equations:
   Case 1: 2x - 5 = 7
   x = 6
   Case 2: 2x - 5 = -7
   Subtract 5 from both sides:
   x = -1
   
4. 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.

• 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.

 

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)
Absolute Value Equation Worksheet #5 |-3x|= 9
Absolute Value Equation Worksheet #6 |y + 4| = 21
Absolute Value Equation Worksheet #7 |3t - 5| = 15
Absolute Value Equation Worksheet #8 |\( \frac{4}{5} \)b| = 32
Absolute Value Equation Worksheet #9 \( \frac{|c + 3|}{4} \)= 12
Absolute Value Equation Worksheet #10 |\( \frac{d}{7} \) + 10| = 28

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

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Solve Absolute Value Equations

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