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How to solve absolute value equations

|x + 5| = 3

Steps

The General Steps to solve an absolute value equation are:

  • Rewrite the absolute value equation as two separate equations, one positive and the other negative
  • Solve each equation separately
  • After solving, substitute your answers back into original equation to verify that you solutions are valid
  • Write out the final solution or graph it as needed

It's always easiest to understand a math concept by looking at some examples so, check outthe many examples and practice problems below.

You can always check your work with our Absolute value equations solver too

Practice Problems

Example Equation

Problem 1

Solve the equation: |X + 5| = 3

Click here to practice more problems like this one, questions that involve variables on 1 side of the equation.

Problem 2

Some absolute value equations have variables both sides of the equation. However, that will not change the steps we're going to follow to solve the problem as the example below shows:

Solve the equation: |3X| = X − 21

Problem 3

Solve the following absolute value equation: | 5X +20| = 80

Problem 4

Solve the following absolute value equation: | X | + 3 = 2X

This first set of problems involves absolute values with x on just 1 side of the equation (like problem 2).

Problem 5

Solve the following absolute value equation: |3X −6 | = 21


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