Absolute Value Inequalities

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

Videos

Solving absolute value inequalities -
Professor Edward Burger explains solving absolute value inequalities.

Professor Edward Burger explains more examples of solving absolute value inequalities.

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