Solving Absolute Value Inequalities

• A
• B
• C
• D

• A
• B
• C
• D

| 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

| -8x | < 8

What is the correct first step?

• separate into two inequalities with an "and"

• separate into two inequalities with an "or"

• divide both sides by -8

• add 8 to both sides

| x - 2 | > 3
Is this an "and"  or an "or" problem?

• and

• or

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

The average temperature in Las Vegas in July is 110 degrees.  If the temperature can vary up to 10 degrees, which equation represents this situation?

• | x - 10 | < 110

• | 110 - x | < 10

• | x - 110 | < 10

• | 10 - x | < 110

Solve:
|x + 3| > - 8

• x > 5 or x < -11

• x > 5

• all real numbers

• no solution