$\begin{array}{1 1} (A)\;(-6,\infty)\\(B)\; (-2,\infty)\\(C)\;(-\infty,-3)\\(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 $'>'$ .

Step 1:

$3x -7+7 > 5x + 6-5x$

Adding 7 to both sides of the inequality

=> $ 3x-7 +7 > 5x -1+7$

=> $ 3x > 5x +6 $

subtracting 5x from both sides of the inequality .

$=> 3x -5x > 5x +6-5x$

=> $ -2x >6$

Dividing both sides by a negetive number -2.

=> $ \large\frac{-2x}{-2} < \frac{6}{-2}$

=> $ x < -3$

Step 2:

All real numbers which are less than $-3$ satisfy the given inequality .

The solution set is $(-\infty, -3)$

Hence C is the correct answer.

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