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##### Intros
###### Lessons
1. $\bullet$ 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:$\heartsuit$ < $-a$ $\;or\;$ $\heartsuit$ > $a$
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##### Examples
###### Lessons
1. Solving Basic Absolute Value Inequalities
Solve:
1. $|x|$ < $4$
$|x| \leq$ $4$
2. $|x|$ > $4$
$|x| \geq$ $4$
2. Solving Absolute Value Inequalities Involving "less than"
Solve: $|2x-1|$ < $3$
1. Solving Absolute Value Inequalities Involving "greater than"
Solve:
1. $|4x-5|$ > $7$
2. $|x|-5 \geq -1$
2. Multiplying/Dividing an Inequality by a Negative Number
Solve:
1. $|3-2x| \leq 11$
2. $|-\frac{x}{6}+\frac{5}{3}|$ > $2$
3. Given a Pair of Inequalities, Determine the Corresponding Absolute Value Inequality
Determine the absolute value inequality statement that corresponds to each inequality:
1. $-1$ < $x$ < $5$
2. $x \leq-10$ $\;or\;$ $x \geq 2$
4. Recognizing Absolute Value Inequalities with "No Solution" or "All Real Numbers"
Solve:
1. $|x+3|$ < $-5$
2. $|x-4|$ > $-1$
###### Topic Notes
$\bullet$ absolute value inequalities: $| \heartsuit |$ < $a$,
solution:$-a$ < $\heartsuit$ < $a$
$\bullet$ absolute value inequalities: $| \heartsuit |$ > $a$,
solution:$\heartsuit$ < $-a$ $\;or\;$ $\heartsuit$ > $a$