Absolute Value Inequalities

Solve:
 |x + 3| > 8

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution

Solve:
|x + 3| > - 8

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution

Solve:
3 | 2x + 7| - 7 < -4

• x < -3 and x > -5/3
• x < -3 and x > -4
• all real numbers
• no solution

Solve:
3 | 2x + 7| + 7 < 4

• x < -3 and x > -5/3
• x < -3 and x > -4
• all real numbers
• no solution

Solve:
|x + 4| + 8 > 2

• x < -3 and x > -5/3
• x < -3 and x > -4
• all real numbers
• no solution

• no solution
• all real numbers 
• -2 ≤ n ≤ 16
• n ≤ -2 or n ≥ 16

Solve.
|y - 4| ≥ 8

• y ≤ -4 or y ≥ 12
• -4 ≤ y ≤ -12
• y ≤ 4 or y ≥ -12
• -12 ≤ x ≤ 4

Solve.
|p + 3| ≥ 10

• -13 ≤ p ≤ 7
• p ≤ -13 or p ≥ 7
• -7 ≤ p ≤ 13
• p ≤ -7 or p ≥ 13

| k - 3 | < -1

• No Solution
• All Real Numbers
• 2 < k < 4
• k < 2  or  k > 4

An absolute value inequality is

• an inequality that contains an absolute value expression
• impossible to solve
• an equation that contains an absolute value expression
• always going to have two solutions