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:
1. $|x|$ < $4$
  $|x| \leq$ $4$
2. $|x|$ > $4$
  $|x| \geq$ $4$
Solving Absolute Value Inequalities Involving "less than"
Solve: $|2x-1|$ $∣2 x - 1∣$ < $3$ $3$
Solving Absolute Value Inequalities Involving "greater than"
Solve:
1. $|4x-5|$ > $7$
2. $|x|-5 \geq -1$
Multiplying/Dividing an Inequality by a Negative Number
Solve:
1. $|3-2x| \leq 11$
2. $|-\frac{x}{6}+\frac{5}{3}|$ > $2$
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. $x \leq-10$ $\;or\;$ $x \geq 2$
Recognizing Absolute Value Inequalities with "No Solution" or "All Real Numbers"
Solve:
1. $|x+3|$ < $-5$
2. $|x-4|$ > $-1$

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