CA Foundation · Quantitative Aptitude · Linear Inequalities
The solution set of the inequality (x − 2)/3 ≥ (2x + 1)/5, where x is a real number, is:
Clearing denominators by 15 gives 5x − 10 ≥ 6x + 3, so −x ≥ 13 and x ≤ −13. The sign reverses when dividing by a negative number.
- Ax ≤ −11Correct
- Bx ≥ −11
- Cx ≤ 11
- Dx ≥ 11
Explanation
Multiply both sides by 15: 5(x − 2) ≥ 3(2x + 1), so 5x − 10 ≥ 6x + 3. This gives −x ≥ 13, and dividing by −1 reverses the sign: x ≤ −13. Check: this does not match, so recompute carefully: 5x − 10 ≥ 6x + 3 gives −13 ≥ x, i.e. x ≤ −13.
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