Question

The solution set of the inequality $37 - (3x + 5) \ge 9x - 8 (x - 3)$ is

• A. $(- \infty, 2)$
• B. $(- \infty, -2)$
• C. $(- \infty, 2]$
• D. $(- \infty, -2]$

Answer 1

Answer: (C)

We have, $37 - (3x + 5) \ge 9x - 8(x - 3)$
$(37 - 3x - 5) \ge 9x - 8x + 24$
$\Rightarrow 32 - 3x \ge x + 24$
Transferring the term $24$ to $L.H.S.$ and the term $(-3x)$ to $R.H.S.$
$32 - 24 \ge x + 3x \Rightarrow 8 \ge 4x \Rightarrow 4x \le 8$
Dividing both sides by 4,
$\frac{4x}{4} \le\frac{8}{4} \Rightarrow x \le 2$

$\therefore $ Solution set is $(-\infty, 2]$.