CA Foundation · Quantitative Aptitude · Linear Inequalities
How many integer values of x satisfy the system 3x − 5 < 2x + 4 and 4x + 1 ≥ x − 8?
There are 12 integer solutions. The inequalities reduce to x < 9 and x ≥ −3, so the integers run from −3 to 8 inclusive. Counting these gives 8 − (−3) + 1 = 12, since 9 is excluded by the strict inequality.
- A12Correct
- B13
- C11
- D14
Explanation
First: 3x − 5 < 2x + 4 gives x < 9. Second: 4x + 1 ≥ x − 8 gives 3x ≥ −9, so x ≥ −3. Integers from −3 to 8 inclusive: 8 − (−3) + 1 = 12. Counting up to 9 would give 13, which wrongly includes the excluded strict bound.
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