# Precalculus : Linear Inequalities

## Example Questions

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### Example Question #2 : Solve Absolute Value Inequalities

Solve the absolute value inequality.

Explanation:

First, simplify so that the absolute value function is by itself on one side of the inequality.

.

Note that the symbol flipps when you divide both sides by .

Next, the two inequalities that result after removing the absolute value symbols are

and   .

When you simplify the two inequalities, you get

and .

Thus, the solution is

.

### Example Question #41 : Inequalities And Linear Programming

Explanation:

To solve absolute value inequalities, you have to write it two different ways. But first, divide out the 4 on both sides so that there is just the absolute value on the left side. Then, write it normally, as you see it:  and then flip the side and make the right side negative: . Then, solve each one. Your answers are and .

### Example Question #42 : Inequalities And Linear Programming

Solve the following:

Explanation:

To solve absolute value inequalities create two functions.

Simply remember that when solving inequalities with absolute values, you keep one the same and then flip the sign and inequality on the other.

Thus,

Then, you must write it in interval notation.

Thus,

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