# Question #5db08

Jul 22, 2016

$x = 1 - \frac{y + 1}{z}$

#### Explanation:

Your starting equation looks like this

$x z + y + 1 = z$

Your goal here is to solve this equation for $x$, which essentially means that you must isolate $x$ on one side of the equation.

The first thing to do here is add $- \left(y + 1\right)$ to both sides of the equation

$x z + \textcolor{red}{\cancel{\textcolor{b l a c k}{y + 1}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(y + 1\right)}}} = z - \left(y + 1\right)$

This is equivalent to

$x z = z - \left(y + 1\right)$

Now all you have to do is divide both sides of the equation by $z$ to get $x$ alone on the left side

$\frac{x \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{z}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{z}}}} = \frac{z - \left(y + 1\right)}{z}$

$x = \frac{z - \left(y + 1\right)}{z} = \frac{z}{z} - \frac{y + 1}{z} = 1 - \frac{y + 1}{z}$
Notice that you need to have $z \ne 0$ in order for this to work.