What value of $x$ is the solution to the equation below? $$-\frac{1}{3}\left(x-\frac{8}{3}x\right)=-5$$

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We could distribute first, but it will get a bit messy.

$$-\frac{1}{3}\left(x-\frac{8}{3}x\right)=-5$$ $$-\frac{1}{3}x+\frac{8}{9}x=-5$$

Depending on how you like to deal with fractions,

$$x=\boxed{-9}$$

Deal with the outer fractional coefficient first by multiplying both sides by $-3$.

$$-\frac{1}{3}\left(x-\frac{8}{3}x\right)=-5$$ $$(-3)\left(-\frac{1}{3}\left(x-\frac{8}{3}x\right)\right)=(-5)(-3)$$ $$x-\frac{8}{3}x=15$$

Again, we have two choices for how to deal with these types of equations.

$$x=\boxed{-9}$$