# How do you solve the equation 5-8z=25+4z?

Feb 7, 2017

See the entire solution process below:

#### Explanation:

First, subtract $\textcolor{red}{5}$ and $\textcolor{b l u e}{4 z}$ from each side of the equation to isolate the $z$ terms while keeping the equation balanced:

$5 - 8 z - \textcolor{red}{5} - \textcolor{b l u e}{4 z} = 25 + 4 z - \textcolor{red}{5} - \textcolor{b l u e}{4 z}$

$5 - \textcolor{red}{5} - 8 z - \textcolor{b l u e}{4 z} = 25 - \textcolor{red}{5} + 4 z - \textcolor{b l u e}{4 z}$

$0 - 12 z = 20 + 0$

$- 12 z = 20$

Now, divide each side of the equation by $\textcolor{red}{- 12}$ to solve for $z$ while keeping the equation balanced:

$\frac{- 12 z}{\textcolor{red}{- 12}} = \frac{20}{\textcolor{red}{- 12}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 12}}} z}{\cancel{\textcolor{red}{- 12}}} = \frac{4 \times 5}{\textcolor{red}{4 \times - 3}}$

$z = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \times 5}{\textcolor{red}{\cancel{4} \times - 3}}$

$z = \frac{5}{-} 3$

$z = - \frac{5}{3}$