Solve the given inequality for real x:


Solve the given inequality for real x:  $\frac{(2 x-1)}{3} \geq \frac{(3 x-2)}{4}-\frac{(2-x)}{5}$


$\frac{(2 x-1)}{3} \geq \frac{(3 x-2)}{4}-\frac{(2-x)}{5}$

$\Rightarrow \frac{(2 x-1)}{3} \geq \frac{5(3 x-2)-4(2-x)}{20}$

$\Rightarrow \frac{(2 x-1)}{3} \geq \frac{15 x-10-8+4 x}{20}$

$\Rightarrow \frac{(2 x-1)}{3} \geq \frac{19 x-18}{20}$

$\Rightarrow 20(2 x-1) \geq 3(19 x-18)$

$\Rightarrow 40 x-20 \geq 57 x-54$

$\Rightarrow-20+54 \geq 57 x-40 x$

$\Rightarrow 34 \geq 17 x$

$\Rightarrow 2 \geq x$

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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