In this lesson, we will look into how to solve absolute value inequalities. Check out the lesson on what is meant by absolute value if necessary.
There are two types of absolute value inequalities, which are solved differently.
The “less than” type
For example:
The “greater than” Type
For example:
Let us first look at the “less than” type.
If the inequality looks like
then the solution looks like
– c < x < c
Example:
Solve
Solution:
–5 < x < 5
Example:
Solve
Solution:
–4 < 2x – 3 < 4
To isolate x, first add 3 to each term of the inequality
–1 < 2x < 7
then divide each term by 2
Now, we will look at the “greater than” type
If the inequality looks like
then the solution looks like
x < – c or x > c
Example:
Solve
Solution:
x < –5 or x > 5
Example:
Solve
Solution:
2x – 3 < –4 or 2x – 3 > 4
To isolate x, first add 3 to each term of the inequality
2x < –1 or 2x > 7
then divide each term by 2
Try out our new and fun Fraction Concoction Game.
Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.