$\begin{array}{1 1}(A)\;[2,8]\\(B)\;[-4,2]\\(C)\;(-23,2]\\(D)\;[2,3]\end{array} $

- 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 $'>'$ .

Step 1 :

Given inequality is $ -15 < \large\frac{3(x-2)}{5}$$ \leq 0$

Multiplying by 5 throughout the inequality $-75 <3 (x-2) \leq 0$

Dividing by 3 throughout the inequality $-25 < x -2 \leq 0$

Adding 2 thoughout the inequality

$-25 +2 < x -2 +2 \leq 0+2$

=> $ -23 < x \leq 2$

Step 2:

All numbers greater than -23 and less than or equal to 2 are solutions to the given inequality .

The solution set is $(-23,2 ]$

Hence C is the correct answer.

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