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CA Foundation · Quantitative Aptitude · Linear Inequalities

If x is a real number satisfying 4 − 5x ≥ 2x − 17, which of the following is the solution set?

The solution set is x ≤ 3. Bringing like terms together gives 21 ≥ 7x, so x ≤ 3. At x = 3 both sides equal −11, confirming that the boundary is included and smaller values satisfy the inequality.

  1. Ax ≥ 3
  2. Bx ≤ 3Correct
  3. Cx ≤ −3
  4. Dx ≥ −3

Explanation

Move terms: 4 + 17 ≥ 2x + 5x, so 21 ≥ 7x, giving x ≤ 3. Check x = 3: LHS = −11, RHS = −11, equality holds. The option x ≥ 3 results from wrongly reversing the sign.

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