Absolute Value Inequalities

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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

Absolute Value Inequality Example
Solve and graph the following inequality: |3x - 6| ≤ 12 Absolute Value Inequality Example
Solve the absolute value inequality: |2x - 5| > 7

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