$\begin{array}{1 1} (A)\;(4,\infty)\\(B)\;(\infty,-6)\\(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 inequlaity is $2(2x+3) -10 < 6 (x-2)$

$=> 4x+6 -10 < 6 (x-2)$

$=> 4x-4 < 6x -12$

Adding 12 on both sides,

$=> 4x-4+12 < 6x-12+12$

Adding $-4x$ on both sides,

=> $4x+8-4x < 6x -4x $

=> $ 8 < 2x$

dividing by a positive number 2 on both sides, => $4 < x$

Step 2:

All numbers greater than $4$ satisfy the given inequality

The solution set is $(4 , \infty)$

Hence A is the correct answer.

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