Numerical answer
How many integers x satisfy |3x + 2| ≤ 20?
Show answer and solution
Answer: 14
|3x + 2| ≤ 20 means −20 ≤ 3x + 2 ≤ 20, i.e. −22 ≤ 3x ≤ 18.
Dividing by 3: −22/3 ≤ x ≤ 6, i.e. −7.33… ≤ x ≤ 6.
The smallest integer satisfying this is −7 (since −22/3 ≈ −7.33), and the largest is 6.
Integer count = 6 − (−7) + 1 = 14.
Tip: for |ax + b| ≤ k, isolate x into a range first and only then round each end inward to the nearest integer — don't round before dividing.
Dividing by 3: −22/3 ≤ x ≤ 6, i.e. −7.33… ≤ x ≤ 6.
The smallest integer satisfying this is −7 (since −22/3 ≈ −7.33), and the largest is 6.
Integer count = 6 − (−7) + 1 = 14.
Tip: for |ax + b| ≤ k, isolate x into a range first and only then round each end inward to the nearest integer — don't round before dividing.
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