Question

An industrial laser cuts steel plates that are 11.93 meters long. The laser can have an error value of at most 0.02 meters.

The inequality |x − | ≤ can be used to find the range of acceptable lengths for the steel plates.
The range of acceptable lengths for the steel plates is ≤ x ≤

Answer 1

• | x - 11.93 | ≤ 0.02
• 11.91 ≤ x ≤ 11.95

Explanation:

Error is the difference from the nominal value, hence the nominal value is what is subtracted from x. We want the magnitude of that difference, | x-11.93 |, to be less than the maximum error value, 0.02, so the inequality is ...

|x -11.93| ≤ 0.02

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We can solve this by "unfolding" it, then adding 11.93:

-0.02 ≤ x -11.93 ≤ 0.02

11.91 ≤ x ≤ 11.95