CA Foundation · Quantitative Aptitude · Linear Inequalities
The solution set of the system 2x + 3 > 7 and 5x − 4 ≤ 21, where x is a real number, is:
The solution is 2 < x ≤ 5. The first inequality reduces to x > 2 and the second to x ≤ 5. Since both must be true at once, we take their intersection, which excludes 2 and includes 5.
- A2 < x ≤ 5Correct
- Bx > 2 or x ≤ 5
- C2 ≤ x < 5
- Dx > 5
Explanation
2x + 3 > 7 gives 2x > 4, so x > 2. 5x − 4 ≤ 21 gives 5x ≤ 25, so x ≤ 5. Both must hold together, so the intersection is 2 < x ≤ 5. The option with 'or' gives all reals, which is wrong because the conditions must hold simultaneously.
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