AlgebraHardCounting integers in a compound inequality
Algebra practice question
How many integer values of x satisfy 7 < 3x − 2 ≤ 16?
Answer: 3
Add 2: 9 < 3x ≤ 18. Divide by 3: 3 < x ≤ 6. The integers are 4, 5, and 6.
Common wrong answers
- If you answered 2
- 2 wrongly excludes x = 6, but the right inequality includes it.
- If you answered 4
- 4 wrongly includes x = 3, but the left inequality is strict.
- If you answered 6
- 6 is the largest solution, not the count.
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