Question:
Solve the given inequality for real $x: 37-(3 x+5) \geq 9 x-8(x-3)$
Solution:
$37-(3 x+5) \geq 9 x-8(x-3)$
$\Rightarrow 37-3 x-5 \geq 9 x-8 x+24$
$\Rightarrow 32-3 x \geq x+24$
$\Rightarrow 32-24 \geq x+3 x$
$\Rightarrow 8 \geq 4 x$
$\Rightarrow 2 \geq x$
Thus, all real numbers $x$, which are less than or equal to 2 , are the solutions of the given inequality.
Hence, the solution set of the given inequality is $(-\infty, 2]$.