# How do you solve and graph z+3>2/3?

Jul 2, 2017

See a solution process below:

#### Explanation:

Subtract $\textcolor{red}{3}$ from each side of the inequality to solve for $z$ while keeping the inequality balanced:

$z + 3 - \textcolor{red}{3} > \frac{2}{3} - \textcolor{red}{3}$

$z + 0 > \frac{2}{3} - \textcolor{red}{3}$

$z > \frac{2}{3} - \textcolor{red}{3}$

To subtract $\textcolor{red}{3}$ from $\frac{2}{3}$ we need to put the $\textcolor{red}{3}$ over a common denominator by multiplying by the appropriate form of $1$:

$z > \frac{2}{3} - \left(\frac{3}{3} \times \textcolor{red}{3}\right)$

$z > \frac{2}{3} - \frac{9}{3}$

$z > \frac{2 - 9}{3}$

$z > - \frac{7}{3}$