Solve the given inequality for real x: 37 ­– (3x + 5) ≥ 9x – 8(x – 3)


Solve the given inequality for real $x: 37-(3 x+5) \geq 9 x-8(x-3)$


$37-(3 x+5) \geq 9 x-8(x-3)$

$\Rightarrow 37-3 x-5 \geq 9 x-8 x+24$

$\Rightarrow 32-3 x \geq x+24$

$\Rightarrow 32-24 \geq x+3 x$

$\Rightarrow 8 \geq 4 x$

$\Rightarrow 2 \geq x$

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 $(-\infty, 2]$.

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