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CA Foundation · Quantitative Aptitude · Linear Inequalities

Solve for real x: (2x + 1)/3 ≥ (x − 2)/2 + 1.

The solution is x ≥ −2. Multiplying by 6, which is positive so the sign stays, gives 4x + 2 ≥ 3x − 6 + 6, that is 4x + 2 ≥ 3x. So x ≥ −2.

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

Explanation

Multiply by 6: 2(2x + 1) ≥ 3(x − 2) + 6, so 4x + 2 ≥ 3x. Hence x ≥ −2. Check: x = −2 gives LHS = −1 and RHS = −2 + 1 = −1, equality holds. Reversing the sign wrongly gives x ≤ −2.

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