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 $(-\infty ,2]$.