Absolute Value Inequalities and Word Problems

• no solution
• a> -1/6 or a< -5/6
• a>1/2 or a< -3/2
• all real numbers

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

• r > 11/4 or r < 9/4
• r > 5 or r ≤ 0
• r > 5 or r < 0
• r < -5 or r > 0

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

• A

• B

• C

• D

• A

• B

• C

• D

Describe the first step in solving the absolute value inequality

• Add 5 on both sides

• Divide both sides by -5

• Set up two inequalities

• no solution

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

• n > 1 or n < -7
• n > -1 or n < -7
• -7 < n < -1
• no solution

Your 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. Write an absolute value equation to model this situation.

• |x-50|=15

• |x+15|=50

• |50+x|=15

• No Solution