# Solving Equations with Absolute Values

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In this lesson we will be looking at solving equations with absolute values on one side of the equation and on both sides of the equation.

## Absolute Values On One Side Of The Equation

When solving an equation with absolute values, it is necessary to split the equation into two equations, one resulting in a positive value and the other resulting in a negative value. We can then solve the two equations to obtain two possible solutions.

*Example: *

Solve

*Solution: *

*x* + 2 = 3 or *x* + 2 = –3

*x* = 1 or *x* = –5 (subtract 2 from both sides)

*Example: *

Solve

*Solution: *

2*x* – 6 = 8 or 2*x* – 6 = –8

2*x* = 14 or 2*x* = –2 (add 6 to both sides)

*x* = 7 or *x* = –1 (divide 2 to both sides)

The following video shows how to solve multi-step equations with absolute values.

**Absolute Values On Both Side Of The Equation**

The same method can be applied when there are absolute values on both side of the equation.

*Example: *

*Solution: *

3*x* + 3 = 2*x* + 5 or 3*x* + 3 = –(2*x* + 5)

**Solving the first equation: **

3*x* + 3 = 2*x* + 5

3*x* – 2*x* = 5 – 3

*x* = 2

**Solving the second equation:**

3*x* + 3 = –(2*x* + 5)

3*x* + 3 = –2*x* – 5

3*x* + 2*x* = –5 –3

5*x* = –8

How to solve equations if there is an absolute value expression on each side of the equation.

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