Solving Absolute Value Inequalities

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 > 6 and x < 10

• x > 6 or x < -14

• all real numbers

• no solution

Solve.
|p + 3| ≥ 10

• -13 ≤ p ≤ 7

• p ≤ -13 or p ≥ 7

• -7 ≤ p ≤ 13

• p ≤ -7 or p ≥ 13

Solve.
|3c - 4| < 12

• -2 2/3 < c < 5 1/3

• c < -5 1/3  or c > 2 2/3

• c < 5 1/3 or c > -2 2/3

• -5 1/3 < c < 2 2/3

Solve.
|4k + 12| ≥ 6

• v ≤ -4.5 or v ≥ -1.5

• -4.5 ≤ v ≤ -1.4

• -1.5 ≤ v ≤ 4.5

• v ≤ -1.5 or v ≥ 4.5

Solve.
6 - 2|m -3| > -4

• -8 < m < 2

• m < -8 or m > 2

• m < -2 or m > 8

• -2 < m < 8

Which compound inequality involves <, ≤ when solving absolute value inequalities?

• and

• or

What kind of compound inequality is this?

• AND compound inequality

• OR compound inequality

Solve.
|c + 4| < 5

• x < -9 or x > 1

• -9 < x < 1

• x < 9 or x > -1

• -1 < x < 9

Solve.
|y - 1| ≤ 6

• -7 ≤ y ≤ 5

• y ≤ -7 or y ≥ 5

• -5 ≤ y ≤ 7

• y ≤ -5 or y ≥ 7