Numerical answer
How many integers x satisfy |3x − 4| ≤ 11?
Show answer and solution
Answer: 8
|3x − 4| ≤ 11 means −11 ≤ 3x − 4 ≤ 11.
Add 4 throughout: −7 ≤ 3x ≤ 15.
Divide by 3: −7/3 ≤ x ≤ 5, i.e. approximately −2.33 ≤ x ≤ 5.
The integers in this range are −2, −1, 0, 1, 2, 3, 4, 5 — that is 8 integers.
Add 4 throughout: −7 ≤ 3x ≤ 15.
Divide by 3: −7/3 ≤ x ≤ 5, i.e. approximately −2.33 ≤ x ≤ 5.
The integers in this range are −2, −1, 0, 1, 2, 3, 4, 5 — that is 8 integers.
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