Question

A company did a quality check on all the packs of nuts it manufactured. Each pack of nuts is targeted to weigh 18.25 oz. A pack must weigh within 0.36 oz of the target weight to be accepted. Find the absolute value inequality that describes the situation and solve it to find the range of rejected masses, x. |x − 18.25| > 0.36; x < 17.89 or x > 18.61 |x − 0.36| + 18.25 > 0; x < 17.89 or x > 18.61 |x − 18.25| > 0.36; x < 18.25 or x > 18.61 |x − 0.36| + 18.25 > 0; x < 18.25 or x > 18.61

Answer 1

Answer: the first choice, |x − 18.25| > 0.36; x < 17.89 or x > 18.61

Step-by-step explanation:

1. Target weight: 18.25 oz

2. Variability accepted: 0.36 oz

3. Range of accepted masses: 18.25 oz - 0.36 oz ≤ x ≤ 18.25 oz + 0.36 oz

4. Addition property of the inequalities (subtract 18.25 oz to the three parts of the inequality):

- 0.36 oz ≤ x - 18.25 oz ≤ 0.36 oz

5. Definition of absolute value inequality: | x - a | ≤ c equals - c ≤ x - a ≤ c

∴ - 0.36 ≤ x - 18.25 ≤ 0.36 equals | x - 18.25 | ≤ 0.36, which is the range of accepted masses.

6. The range of rejected masses is the complement, so it is:

|x - 18.25 | > 0.36

7. Solve the inequality to find the range of rejected masses:

a) x - 18.25 > 0.36 ⇒ x > 18.25 + 0.36 ⇒ x > 18.61

b) x - 18.25 < 0.36 ⇒ x < 18.25 - 0.36 ⇒ x < 17.89