Advanced MathMediumSolution set of an absolute-value inequality
Advanced Math practice question
The function h is defined by h(x) = |x − 5|. Which of the following describes all values of x for which h(x) ≤ 2?
- A. 3 ≤ x ≤ 7Correct
- B. x ≤ 7
- C. x ≤ 3 or x ≥ 7
- D. −7 ≤ x ≤ −3
Answer: A. 3 ≤ x ≤ 7
|x − 5| ≤ 2 means −2 ≤ x − 5 ≤ 2, so 3 ≤ x ≤ 7.
Why the other answers are wrong
- B. x ≤ 7
- x ≤ 7 includes values like 0, where |0 − 5| = 5 > 2.
- C. x ≤ 3 or x ≥ 7
- Those are the values where h(x) ≥ 2, the outside of the interval.
- D. −7 ≤ x ≤ −3
- The signs are reversed; the interval is centred on 5.
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