Absolute+Value+Inequalities

Absolute Value Inequalities

Isolate the absolute value Split using "and" or "or" (and for < __<__, or for > __>__ =) Graph the compound inequality Describe solution set algebraically

x+4 < 3 and x+4 > -3 x < -1 and x > -7  -1 > x > -7
 * 1.** I x+4 I < 3

x-1 > -3 or x-1 < 3 x > -2 or x < 4  all real numbers
 * 2.** I x-1 I > -3

-2 I x+1 I > 4 I x+1 I < -2 x+1 < -2 and x+1 > 2 x 1 null set
 * 3.** -2 I x+1 I -3 > 1

-3 I 2x-1I < -15 I 2x-1I > 5 2x-1 > 5 or 2x-1 < -5 2x > 6 or 2x < -4 x > 3 or x < -2  x > 3 or x < -2
 * 4.** -3 I 2x-1I +5 < -10

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