Solving Absolute Value Inequalities and Understanding Transformations

| 2w - 1 | < 11

• No Solution

• All Real Numbers

• -5 < w < 6

• -6 < w < 5

| x + 1 | ≥ 3

• No Solution

• All Real Numbers

• x ≤ -4  or  x ≥ 2

• -4 ≤ x ≤ 2

Solve the absolute Value inequality and graph. 

• A

• B

• C

• D

• no solution
• a> -1/6 or a< -5/6
• a>1/2 or a< -3/2
• all real numbers

no solution

• no solution

• x > 2 or x < -22

• -22 < x < 2

• all real numbers

• A
• B
• C
• D

• A
• B
• C
• D

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

| 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