If \(\displaystyle\frac{3x-5}{6}+8\ge 4+\frac{2x}{3}\), then
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(x \in (-\infty, 19]\)
Multiplying both sides by 6, a positive number, keeps the inequality sign:
\(3x - 5 + 48 \ge 24 + 4x\)
\(3x + 43 \ge 24 + 4x\)
\(43 - 24 \ge 4x - 3x\)
\(19 \ge x\)
So \(x \le 19\), that is, \(x \in (-\infty, 19]\).