# Solving absolute value inequalities

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##### Intros

###### Lessons

- $\bullet$ definition of absolute value: $| \heartsuit | =$
**distance of**$\heartsuit$**from zero**

$\bullet$**absolute value inequalities:**$| \heartsuit |$ < $a$,**solution:**$-a$ < $\heartsuit$ < $a$

$\bullet$**absolute value inequalities:**$| \heartsuit |$ > $a$,**solution:**$\heartsuit$ < $-a$ $\;or\;$ $\heartsuit$ > $a$

##### Examples

###### Lessons

**Solving Basic Absolute Value Inequalities**

Solve:**Solving Absolute Value Inequalities Involving "less than"**

Solve: $|2x-1|$ < $3$**Solving Absolute Value Inequalities Involving "greater than"**

Solve:**Multiplying/Dividing an Inequality by a Negative Number**

Solve:**Given a Pair of Inequalities, Determine the Corresponding Absolute Value Inequality**

Determine the absolute value inequality statement that corresponds to each inequality:**Recognizing Absolute Value Inequalities with "No Solution" or "All Real Numbers"**

Solve: