Solve Absolute Value Inequalities and Word Problems and Evaluate Piecewise Functions

• 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

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

A company sells 20-ounce bottles of sports drink. The actual volume of liquid in the bottle must be within 0.03 ounces. What equation can be solved to find the minimum and maximum volume of liquid in a bottle.

• |v|-20=0.03
• |v-20|=0.03
• |v|-0.03=20
• |v-0.03|=20

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 street width below would NOT have to be repaired?

• 24 feet, 10 inches

• 24 feet, 3 inches

• 25 feet, 7 inches

• 25 feet, 11 inches

John is looking for a job after graduation. The salary which he is satisfied with must be $3000 with a tolerance of $500. Choose the salary John would accept.

• $3,478
• $3,792
• $2,489
• $2,256

Solve:
3 | 2x + 7| - 7 < -4

• x < -3 and x > -5/3
• x < -3 and x > -4
• all real numbers
• no solution

Solve.
|d + ⅔| + ¾ = 0

• no solution
• d = -9 or ½
• d = -¾ or d = 9
• d = -1/12 or d = -7/12