Solving Absolute Value Inequalities Live

| x + 3 | ≤ 2

• No Solution

• x ≤ -1

• -5 ≤ x and x ≤ -1

• 1 ≤ x and x ≤ 5

| 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

Solve for n.

• n ≥ 10 and n ≤ -6

• n > 10 and n < -6

• n ≥ 10 or n ≤ -6

• n > 10 or n < -6

Solve for r.

• r ≥ -38 and r ≤ 32

• r > -38 and r < 32

• r ≥ -38 or r ≤ 32

• r > -38 or r < 32

The radius of the gears produced at a factory must be 6 inches in length with a tolerance of 0.1 inches. The gears with radius beyond the tolerated lengths will be thrown away. Which of the following inequalities can be used to assess which gears are eligible? (x is the length of the radius)

• |x – 6| ≤ 0.1

• |x – 6| ≥ 0.1

• |x – 0.1| ≤ 6

• |x – 0.1| ≥ 6

• no solution
• -6 ≤ r ≥ 8
• 6 > r > -8
• -6 < r < 8

• r > 11/4 or r < 9/4
• r > 5 or r ≤ 0
• r > 5 or r < 0
• r < -5 or r > 0

Solve for x.

• x ≥ -3.33 and x ≤ 2

• x > -3.33 and x < 2

• x ≥ -3.33 or x ≤ 2

• x > -3.33 or x < 2

| x - 2 | > 3

• 2 < x < 10

• x < 2 or x > 10

• -1 < x < 5

• x < - 1 or x > 5