Mastering Absolute Value Inequalities & Number Lines

1. A temperature can vary by 5 degrees from 20 degrees. Write an absolute value inequality to represent this situation and identify the range of temperatures on a number line.

• |T - 20| ≤ 5; Range: 15 ≤ T ≤ 25

• |T - 20| = 5; Range: T = 15 or T = 25

• |T - 20| ≥ 5; Range: T ≤ 15 or T ≥ 25

• |T - 20| < 5; Range: 15 < T < 25

2. A car's speedometer shows that the car is traveling at 60 miles per hour, but it could be off by 10 miles per hour. Write an absolute value inequality to express the possible speeds of the car and identify the solutions on a number line.

• |x - 50| ≤ 10

• |x - 60| ≤ 10

• |x + 60| ≤ 10

• |x - 60| < 10

3. A student scored 85 on a test, and the teacher said the score could be off by 7 points. Write an absolute value inequality to represent the possible scores and show the solutions on a number line.

• |x - 90| ≤ 7

• |x + 85| ≤ 7

• |x - 85| ≤ 7

• |x - 85| < 7

4. A store is having a sale where the price of an item can be $30 plus or minus $5. Write an absolute value inequality for the price range and identify the solutions on a number line.

• |x - 25| ≤ 5

• |x - 30| ≤ 5

• |x - 35| ≥ 5

• |x + 30| ≤ 5

5. A runner's time for a race is 12 minutes, but it could vary by 2 minutes. Write an absolute value inequality to represent the possible times and show the solutions on a number line.

• |t - 12| ≥ 2; Possible times: 8 to 16 minutes.

• |t - 12| = 2; Possible times: 10 or 14 minutes.

• |t - 12| < 2; Possible times: 11 to 13 minutes.

• |t - 12| ≤ 2; Possible times: 10 to 14 minutes.

6. A bank account balance is $200, but it can fluctuate by $50. Write an absolute value inequality to express the possible balances and identify the solutions on a number line.

• |x - 250| ≤ 50

• |x + 200| ≤ 50

• |x - 150| ≤ 50

• |x - 200| ≤ 50

7. A person is standing 3 feet away from a wall and can move 1 foot closer or further away. Write an absolute value inequality to represent the distance from the wall and identify the solutions on a number line.

• |d + 3| ≤ 1

• |d - 4| ≤ 1

• |d - 3| ≤ 1

• |d - 2| ≤ 1

8. A factory produces items with a target weight of 50 grams, but the weight can vary by 4 grams. Write an absolute value inequality to express the acceptable weight range and show the solutions on a number line.

• |x - 50| ≥ 4

• |x - 46| ≤ 4

• |x + 50| ≤ 4

• |x - 50| ≤ 4

9. A cyclist's average speed is 15 miles per hour, but it can vary by 3 miles per hour. Write an absolute value inequality to represent the possible speeds and identify the solutions on a number line.

• |x - 15| < 3; Possible speeds: 13 < x < 17

• |x - 15| ≥ 3; Possible speeds: x ≤ 12 or x ≥ 18

• |x - 15| = 3; Possible speeds: x = 12 or x = 18

• |x - 15| ≤ 3; Possible speeds: 12 ≤ x ≤ 18

10. A book's price is $25, but it can be discounted by up to $3. Write an absolute value inequality to express the possible prices and show the solutions on a number line.

• |x + 25| ≤ 3

• |x - 20| ≤ 3

• |x - 28| ≤ 3

• |x - 25| ≤ 3