 # 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:

2x – 6 = 8 or 2x – 6 = –8

2x = 14 or 2x = –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:

3x + 3 = 2x + 5 or 3x + 3 = –(2x + 5)

Solving the first equation:

3x + 3 = 2x + 5

3x – 2x = 5 – 3

x = 2

Solving the second equation:

3x + 3 = –(2x + 5)

3x + 3 = –2x – 5

3x + 2x = –5 –3

5x = –8 How to solve equations if there is an absolute value expression on each side of the equation.

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