Absolute Value Equations: How to solve absolute value equations

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How to solve absolute value equations

Absolute Value Equations Worksheet (pdf with answer key on this page's topic)
Related: | how to solve absolute value inequalities

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 out both of the examples below.

Absolute Value Equations Solver

Enter any any values and this solver will calculate the solution(s) for your equation and show all work, inccluding checking for extraneous solutions!

|AX + B | = D

Solve My Absolute Value Equation

Example Equation 1

Solve the equation:

|X + 5 | = 3

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

Example Equation 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

|3X| = X − 21

Practice Problems #1

Problem 1) Solve the following absolute value equation:

| 5X +20| = 80

Practice Problems #2

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

Problem 1) Solve the following absolute value equation:

| X | +3 = 2X

Problem 2) Solve the following absolute value equation:

|3X −6 | = 21

Absolute Value Equations Worksheet (pdf with answer key on this page's topic)
Related: | how to solve absolute value inequalities | Images of absolute value Equations