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

Linear Inequalities

Solution:

We have, $37-(3 x+5) \geq 9 x-8(x-3)$
$(37-3 x-5) \geq 9 x-8 x+24$
$\Rightarrow 32-3 x \geq x+24$
Transferring the term 24 to L.H.S.
and the term $(-3 x )$ to $R . H .S$
$32-24 \geq x+3 x$
$ \Rightarrow 8 \geq 4 x $
$\Rightarrow 4 x \leq 8$
Dividing both sides by 4 $\frac{4 x}{4} \leq \frac{8}{4} $
$\Rightarrow x \leq 2$
image
$\therefore $ Solution set is $(-\infty, 2]$