Solve Absolute Value Inequalities and 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

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

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

Solve the absolute Value inequality and graph. 

• A

• B

• C

• D

• v>5 or v<-5
• v≥5 or v≤-5
• v>-5 or v<5
• all real numbers

• A

• B

• C

• D

Solve the inequality.

• A

• B

• C

• D

• no solution
• -6 < x < 26
• x < -6 or x > 26
• all real numbers

Solve the inequality.

• A

• B

• C

• D

• x > 11 or x < 5
• x > - 11 or x > 5
• 5 < x < 11
• - 5 < x < 11