$\begin{array}{1 1}(A)\;(0,1]\\(B)\;[4,5]\\(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 $'>'$ .

The given inequality is $6 \leq -3(2x-4) < 12$

Dividing by a positive numbers 3, through out the inequality

=> $ 2 \leq -(2x-4) <4$

Dividing by a negative number -1 throughout inequality

=> $-2 \geq 2x-4 > -4$

Adding +4 to the inequality through out

$=> -2+ 4 \leq 2x-4+4 > -4+4$

$=> 2 \geq 2x > 0$

Dividing by 2 throughout $ 1 \geq x > 0$

$=> 1 \geq x >0$

Step 2:

All real number greater than or equal to 1 and less than 0 are solutions to the given inequality .

The solution set is $(0,1]$

Hence A is the correct answer.

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