$\begin{array}{1 1}(A)\;[2,8]\\(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 $'>'$ .

Step 1:

The given inequality is $ 2 \leq 3x-4 \leq 5$

Adding $+4$ throughout the inequality $2+4 \leq 3x -4 +4 \leq 5+4$

=> $ 6 \leq 3x \leq 9$

Dividing by positive number 3 through out the inequality $=> 2 \leq x \leq 3$

$=> 2 \leq x \leq 3$

Step 2:

Thus all real number , which are greater than or equal to 2, and less than or equal to 3, are solutions to the given inequality .

The solution set is $ [2,3]$

Hence D is the correct answer.

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