#### Answer

$$x = -20$$
To check if the solution is correct, we plug $-20$ into the original equation and see if both sides of the equation are equal:
$$(\frac{4}{5})(-20) = -16$$
Multiply the left-hand side to get:
$$-16 = -16$$
The two sides are equal, so the solution is correct.

#### Work Step by Step

To solve this equation, we isolate $x$ on one side of the equation. We do that by dividing by $\frac{4}{5}$:
$$x = -16 \div \frac{4}{5}$$
To divide by a fraction means to multiply by its inverse. The inverse of $\frac{4}{5}$ is $\frac{5}{4}$. So we have:
$$x = -16(\frac{5}{4})$$
Solve for $x$ by dividing out common factors:
$$x = -20$$
To check if the solution is correct, we plug $-20$ into the original equation and see if both sides of the equation are equal:
$$(\frac{4}{5})(-20) = -16$$
Multiply the left-hand side to get:
$$-16 = -16$$
The two sides are equal, so the solution is correct.