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

Step 1:

The given inequality is $-3 \leq 4 - \large\frac{7x}{2} $$ \leq 18$

Adding -4 through out the inequality $=> -3-4 \leq 4 - \large\frac{7x}{2} $$-4 \leq 18-4$

=> $ -7 \leq \large\frac{-7x}{2} $$ \leq 14$

Multiplying by a negative number -2 through out

$=> 14 \geq 7x \geq -28$

Dividing by 7 through out the inequality => $ 2 \geq x \geq -4$

Step 2:

All numbers less than or equal to 2 and greater than or equal to -4 are solutions to given inequality .

The solution set is $[-4,2]$

Hence B is the correct answer.

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