# How do you solve and check your solutions to -4/3=2/3z?

Dec 21, 2016

$z = - 2$

#### Explanation:

First, I would multiply each side of the equation by $3$ to eliminate the fraction and keep the equation balanced. This will make the equation easier to work with:

$3 \times - \frac{4}{3} = 3 \times \frac{2}{3} z$

$- \frac{3 \times 4}{3} = \frac{3 \times 2}{3} z$

$- \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \times 4}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \times 2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} z$

$- 4 = 2 z$

Now. we can solve for $z$ while keeping the equation balanced:

$- \frac{4}{\textcolor{red}{2}} = \frac{2 x}{\textcolor{red}{2}}$

$- 2 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} z}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}}$

$- 2 = z$ or $z = - 2$