$\begin{array}{1 1} (A)\;x \in (-6,\infty)\\(B)\;x \in (-2,\infty)\\(C)\;x \in (-4,\infty)\\(D)\;x \in (-9,\infty)\end{array} $

- 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:

$4x+3 < 5x+ 7$

adding -7 to both sides

=> $4x+3-7 < 5x+7-7$

=> $ 4x-4 < 5x$

adding $-4x $ to both sides

=> $ -4 < 5-4x$

=> $ -4 < x $

Step 2:

All real numbers which are greater than $-4$ are the solution for the inequality .

The solution set is $x \in (-4,\infty)$

Hence C is the correct answer.

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