$\begin{array}{1 1} (A)\;(-3,\infty)\\(B)\;(-\infty,2)\\(C)\;(-4,\infty)\\(D)\; (-9,\infty)\end{array} $

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- Same Quantity can be added (a subtracted ) to (from ) both sides of the inequality with out changing the sign of the in equality.
- Same positive quantities can be multiplied or divided to both side of the in equality with out changing the sign of the inequality.
- If same negative quantity is multiplied or divided to both sides of the inequality is reversed i.e $ '>'$ sign changes to $'<' $ and $'<'$ changes $'>'$ .

The given inequality $\large\frac{3(x-2)}{5}$$ \leq 5 \bigg( \large\frac{2-x}{3}\bigg)$

Multiplying both sides of the inequality by 15.

$=> \large\frac{3(x-2)}{5} $$ \times 15 \leq \large\frac{5(2-x)}{3}$$ \times 15$

=> $ 9(x-2) \leq 25 (2-x)$

=> $ 9x -18 \leq 50 -25 x$

Adding 25 x to both sides of the inequality => $9x-18+25 x \leq 50$

Adding 18 to both sides of inequality

$=> 9x +25 x \leq 50+18$

$=> 34 x \leq 68$

dividing x by 34 on both sides,

$=> \large\frac{34 x}{34} \leq \frac{68}{34}$

$ x \leq 2$

Step 2:

All real number less than or equal to $2$ satisfy the given inequality

The solution set is $(-\infty ,2]$

Hence B is the correct answer.

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