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

Summary Submit Skip Question

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.

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