Absolute Value Tolerance

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 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) .

• |25 - W| ≤ .5

• |W - .5| ≤ 25

• |W - 25| ≥ .5

• |.5 - W| ≥ 25

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. The number 15 best represents the...

• range

• tolerance

• optimal or average value

• maximum

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

| -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

At the TX Design Company, the average starting salary for a new designer is $33,600, but the actual salary could differ from the average by as much as $1,560. Which inequality could be used to determine if a salary, x, falls within this range?

•   |x -­ 1,560| ≤ 33,600

•   x -­ 33,600 ≤ 1,560

•   |x ­ -33,600| ≥ 1,560

•   |x -­ 33,600| ≤ 1,560

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.

Solve the absolute Value inequality and graph. 

• A

• B

• C

• D

The graphed solution represents the solutions to which inequality?

• | x + 9 | > 3

• | x - 9 | > 3

• | x - 9 | < 3

• | x + 9 | < 3

| 2w - 1 | < 11

• No Solution

• w < 5

• -5 < w and w < 6

• -6 < w and w < 5