Absolute Value Inequalities and Word Problems

| x + 3 | ≤ 2

• No Solution

• All Real Numbers

• -5 ≤ x ≤ -1

• 1 ≤ x ≤ 5

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

• and

• or

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

• and

• or

| x + 1 | ≥ 3

• No Solution

• All Real Numbers

• x ≤ -4  or  x ≥ 2

• -4 ≤ x ≤ 2

A company makes boxes of crackers that should weigh 213g. A quality control inspector randomly selects boxes to weigh.  Any box that varies from the weight by more than 5g is sent back. What is an equation that shows the range of allowable weights for a box of crackers and what is the range?

• |w - 213| ≤ 5,         208 ≤ w ≤ 218

• |w - 213| ≤ 5,                   0 ≤ w ≤ 10

• |w - 5| ≤ 213,         208 ≤ w ≤ 218

• |w - 5| ≤ 213,                   0 ≤ w ≤ 10

A company that makes golf balls needs to ship bags of balls that contain 690 balls, plus or minus six balls. Write an absolute value inequality that expresses the acceptable number of balls in each bag.

• 690

• 6

• 696

• -6

• 5

• 4

• 3

• 2

• 1

• 689

John is looking for a job after graduation. The salary which he is satisfied with must be $3000 with a tolerance of $500. Which of the following inequalities can be used to assess which if his salary is tolerable? (m is the measure of the salary)

• |m - 500| ≤ 3000

• |m - 500| ≥ 3000

• |m - 3000| ≥ 500

• |m - 3000| ≤ 500

A candy manufacture puts 240 pieces of candy into each bag. The bag can be off by 8 pieces. Write an absolute value inequality that displays the acceptable amount of candy pieces that can be in a bag.

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