Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityMedium
A production line worker is checking product dimensions. The required length of a component is 15.2 cm. Due to manufacturing variations, the actual length can deviate by at most 0.15 cm. Which inequality represents the acceptable range of lengths (L) for the component?
- A15.05 ≤ L ≤ 15.35
- B15.15 ≤ L ≤ 15.25
- C|L - 0.15| ≤ 15.2
- D15.2 - 0.15 > L or L > 15.2 + 0.15
Show answer & explanationAnswer & explanation
Correct answer: A. 15.05 ≤ L ≤ 15.35
The required length is 15.2 cm and the maximum deviation (tolerance) is 0.15 cm. The lowest acceptable length is 15.2 - 0.15 = 15.05 cm. The highest acceptable length is 15.2 + 0.15 = 15.35 cm. Therefore, the acceptable range is 15.05 ≤ L ≤ 15.35.
Why the other options are wrong
- B. This implies a tolerance of 0.05 cm, not 0.15 cm.
- C. This is an incorrect absolute value inequality; it reverses the role of the ideal value and tolerance.
- D. This inequality represents values *outside* the acceptable range, not within it.
Range with Tolerance
When an ideal value has a tolerance, the acceptable range is found by subtracting the tolerance from the ideal value for the lower bound and adding the tolerance to the ideal value for the upper bound.
- Lower Bound = Ideal Value - Tolerance
- Upper Bound = Ideal Value + Tolerance
- The range is expressed as Lower Bound ≤ Variable ≤ Upper Bound
Memory trick: Tolerance: Give or take, a little wiggle room.