To solve this inequality, we first find the critical points by setting the numerator and the denominator equal to zero:

-7 = 0 (numerator cannot equal zero)
x + 3 = 0
x = -3

So the critical point is x = -3.

Next, we test the intervals created by the critical point on the inequality:

1) Test x = -4:
(-7)/(-4 + 3) = -7/(-1) = 7 > 0
Therefore, x = -4 is not a solution.

2) Test x = -2:
(-7)/(-2 + 3) = -7/1 = -7 < 0
Therefore, x = -2 is a solution.

Finally, we write the solution in interval notation:

The solution to the inequality is [ -3, ∞).