Absolute Value Equation and Inequality Word Problems

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

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

To make cocoa powder, cocoa beans are roasted. The ideal temperatures for roasting is 300 degrees Fahrenheit, plus or minus 25 degrees Fahrenheit. Write an equation describing the maximum and minimum temperatures for cocoa beans.

• |x - 300|=25

• |x + 300|=25

• |x - 25|=300

• |x + 25|=300

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

• and

• or

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

• no solution
• x > 2 or x < -22
• -22 < x < 2
• all real numbers

| x - 6 | < 4
Is this an "and"  or an "or" problem?

• and

• or

| 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