Solve for x.

\large \frac{-14}{x}=\frac{-22}{x+4}

To solve for $x$, we can cross multiply:

$$-14(x+4) = -22x$$
$$-14x - 56 = -22x$$

Now, let's isolate $x$ on one side of the equation:

$$-56 = -22x + 14x$$
$$-56 = -8x$$
$$x = \frac{56}{8}$$
$$x = 7$$

Therefore, the solution to the equation is $x = 7$.