# How do you solve 1/2z+1/3=-2/5?

Apr 23, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{30}$ to eliminate the fractions while keeping the equation balanced. $\textcolor{red}{3}$ is the Lowest Common Denominator of the three fractions:

$\textcolor{red}{30} \left(\frac{1}{2} z + \frac{1}{3}\right) = \textcolor{red}{30} \cdot - \frac{2}{5}$

$\left(\textcolor{red}{30} \cdot \frac{1}{2} z\right) + \left(\textcolor{red}{30} \cdot \frac{1}{3}\right) = \cancel{\textcolor{red}{30}} 6 \cdot - \frac{2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}}$

$\left(\cancel{\textcolor{red}{30}} 15 \cdot \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} z\right) + \left(\cancel{\textcolor{red}{30}} 10 \cdot \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}\right) = 6 \cdot - 2$

$\left(15 \cdot 1 z\right) + \left(10 \cdot 1\right) = - 12$

$15 z + 10 = - 12$

Next, subtract $\textcolor{red}{10}$ from each side of the equation to isolate the $z$ term while keeping the equation balanced:

$15 z + 10 - \textcolor{red}{10} = - 12 - \textcolor{red}{10}$

$15 z + 0 = - 22$

$15 z = - 22$

Now, divide each side of the equation by $\textcolor{red}{15}$ to solve for $z$ while keeping the equation balanced:

$\frac{15 z}{\textcolor{red}{15}} = - \frac{22}{\textcolor{red}{15}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{15}}} z}{\cancel{\textcolor{red}{15}}} = - \frac{22}{15}$

$z = - \frac{22}{15}$

Apr 23, 2017

$z = - \frac{22}{15}$

#### Explanation:

First, let's multiply all terms by 30 to remove the fractions.
Doing this, we get:
$15 z + 10 = - 12$

Then, we simplify.
$15 z = - 22$

$z = - \frac{22}{15}$