Inequalities Involving Absolute Value

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

| 2w - 1 | < 11

• No Solution

• w < 5

• -5 < w and w < 6

• -6 < w and w < 5

| x + 3 | > 8

• No Solution

• All Real Numbers

• x < -11  or  x > 5

• -5 < x < 11

| 3x - 9 | < 3

• x < - 10 or x > - 2

• -10 < x < - 2

• x < 2 or x > 4

• 2 < x < 4

Describe the first step in solving the absolute value inequality

• Add 5 on both sides

• Divide both sides by -5

• Set up two inequalities

• no solution

|-9v| < 54

• -6<v<6

• v<-6 or v>6

• v=6 or v=-6

• -6>v<6

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

• x ≤ -1

• -5 ≤ x and x ≤ -1

• 1 ≤ x and x ≤ 5

Solve.
|y - 4| ≥ 8

• y ≤ -4 or y ≥ 12

• -4 ≤ y ≤ -12

• y ≤ 4 or y ≥ -12

• -12 ≤ x ≤ 4

What is the correct first step?

• divide by 10

• multiply by 10

• make it two inequalities with an "or"

• make it two inequalities with and "and"