Solve the linear inequality: (2x - 1) / 3 ≤ (x + 4) / 2.
Answer and explanation
Correct answer: B. x ≤ 14
- Step 1: Clear fractions by multiplying both sides by 6 (LCM of 3 and 2): 6 × [(2x - 1)/3] ≤ 6 × [(x + 4)/2]. Step 2. Expand: 2(2x - 1) ≤ 3(x + 4) => 4x - 2 ≤ 3x + 12. Step 3. Rearrange: 4x - 3x ≤ 12 + 2 => x ≤ 14. Answer: x ≤ 14. Why not the others: x ≥ 14 reverses the inequality sign; x ≤ 10 and x ≥ 10 result from forgetting to multiply 4 by 3.
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