Solve Absolute Value Inequalities and Word Problems

You have money in your wallet, but you don't know the exact amount. When a friend asks you, you say that you have 50 dollars give or take 15. What absolute value inequality describes this situation?

• | x - 15 | ≤ 50

• | x - 50 | ≤ 15

• | x - 15 | ≥ 50

• | x - 50| ≥ 50

Which statement is false regarding this model?  |x - 3.5| > 1

• Tolerance = 1

• The Ideal Amount = 3.5

• The solution to the inequality will be the set of ACCEPTED weights of the toothpick boxes.

• The solution to the inequality will be the set of REJECTED weights of the toothpick boxes.

The graphed solution represents the solutions to which inequality?

• | x + 9 | > 3

• | x - 9 | > 3

• | x - 9 | < 3

• | x + 9 | < 3

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

no solution

• no solution

• x > 2 or x < -22

• -22 < x < 2

• all real numbers

• A
• B
• C
• D

The street built in the city must be 25 feet in width with a tolerance of 0.5 feet. Streets that are not within the tolerated widths must be repaired. Which of the following inequalities can be used to assess which streets are within tolerance? (W is the width of the street) .

• |W - 25| ≤ .5

• |W - .5| ≤ 25

• |W - 25| ≥ .5

• |W - .5| ≥ 25

| 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

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

• and

• or