Question

The net weight on a box of cereal says 14.5 ounces. However, the factory considers any box within 0.25 ounces acceptable to sell
Part 1:
Identify the inequality that represents the scenario described above
Part 2: Solve the inequality from Part 1. Include all your work in your solution

Answer 1

Let x = the net weight (in ounces).

Part 1:
The acceptable condition is that x is within 0.25 oz of 14.5, so
|x − 14.5| ≤ 0.25.

Part 2 (solve):
|x − 14.5| ≤ 0.25 is equivalent to the compound inequality
−0.25 ≤ x − 14.5 ≤ 0.25.
Add 14.5 to all parts:
14.5 − 0.25 ≤ x ≤ 14.5 + 0.25
14.25 ≤ x ≤ 14.75.

So any box with net weight x in the interval [14.25, 14.75] ounces is acceptable.