Solving Equations with Absolute Values

Related Topics:
More Lessons for Algebra

Math Worksheets

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.

Check out our most popular games!
Fraction Concoction	Fact Family Game	Number Bond Garden
Online Addition Subtraction Game	Penguin Solitaire	Sawayama Solitaire
Ark Solitaire	Eldritch Invasion	Shenzhen Solitaire

Check out more Solitaire games here.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.