Absolute Value Inequalities

Solve:
 |x + 3| > 8

• x > 5 or x < -11

• x > 5

• 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

| n + 2 | - 3 ≥ -6

• No Solution

• All Real Numbers

• n ≤ -5  or  n ≥ 1

• -5 ≤ n ≤ 1

Solve.
|c + 4| < 5

• x < -9 or x > 1

• -9 < x < 1

• x < 9 or x > -1

• -1 < x < 9

| x + 3 | ≤ 2

• No Solution

• All Real Numbers

• -5 ≤ x ≤ -1

• 1 ≤ x ≤ 5

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

| 3x - 9 | < 3

• x < - 10 or x > - 2

• -10 < x < - 2

• x < 2 or x > 4

• 2 < x < 4

| 2w - 1 | < 11

• No Solution

• w < 5

• -5 < w and w < 6

• -6 < w and w < 5