OML Search

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.


 

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

OML Search

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

[?] Subscribe To This Site

XML RSS
follow us in feedly
Add to My Yahoo!
Add to My MSN
Subscribe with Bloglines



Math TutorsMath Tutors