Introductory Algebra for College Students (7th Edition)

$$x = -20$$ 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.
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.