Absolute Value Inequalities and Word Problems

The graphed solution represents the solutions to which inequality?

• | x + 9 | > 3

• | x - 9 | > 3

• | x - 9 | < 3

• | x + 9 | < 3

Sam's house is 14 blocks from the school. Emily lives 6 blocks from Sam. Which equation represents the location of Emily's house in relation to the school?

• |x + 6| = 10

• |x – 6| = 14

• |x – 14| = 6

• |x + 14| = 6

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

• and

• or

The radius of the gears produced at a factory must be 6 inches in length within a tolerance of 0.1 inches.

• |x – 6| ≤ 0.1

• |x – 6| ≥ 0.1

• |x – 0.1| ≤ 6

• |x – 0.1| ≥ 6

| 2x + 12 | < 8
Which is the correct first step?

• 2x + 12 < 8 and 2x+12 >-8

• 2x + 12 < 8 or 2x+12 >-8

• 2x + 12 < 8 and 2x+12 <-8

• 2x + 12 < 8 or 2x+12 >-8

Which compound inequality involves <, ≤ when solving absolute value inequalities?

• and

• or

What kind of inequality is this? |x-2|<7

• AND compound inquality

• OR compound inequality

| x + 3 | ≤ 2

• No Solution

• x ≤ -1

• -5 ≤ x and x ≤ -1

• 1 ≤ x and x ≤ 5

Solve for r.

• r ≥ -38 and r ≤ 32

• r > -38 and r < 32

• r ≥ -38 or r ≤ 32

• r > -38 or r < 32

• A
• B
• C
• D