# How do you solve for r in r/n+s=t?

Mar 7, 2018

$r = n t - n s$

#### Explanation:

The algebraic equation we have is:

$\frac{r}{n} + s = t$

We can solve this by:

1) Subtract $s$ from each side

$\to \frac{\textcolor{b l u e}{r}}{n} + s \textcolor{red}{- s} = t \textcolor{red}{- s}$

$\to \frac{\textcolor{b l u e}{r}}{n} = t - s$

2) Multiply each side by $n$

$\to \frac{\textcolor{b l u e}{r}}{n} \textcolor{red}{\cdot n} = \left(t - s\right) \textcolor{red}{\cdot n}$

$\to \textcolor{b l u e}{r} = \left(t - s\right) n$

$\textcolor{b l u e}{r} = n t - n s$

Thus, we have the answer:

$r = n t - n s$