# How do you solve for r in ax + r = 7?

Jun 1, 2016

See explanation

#### Explanation:

Given:$\text{ } a x + r = 7$
$\textcolor{g r e e n}{\text{Using shortcut - based on consequence of first principles}}$

Move $+ a x$ to the other side of the = but change the sign to minus

$\textcolor{b r o w n}{+ a x + r = 7} \textcolor{b l u e}{\text{ "->" } r = 7 - a x}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{g r e e n}{\text{Using first principles}}$

Subtract $\textcolor{b l u e}{a x}$ from $\underline{\text{both sides.}}$

$\textcolor{b r o w n}{a x + r \textcolor{b l u e}{- a x} = 7 \textcolor{b l u e}{- a x}} \textcolor{m a \ge n t a}{\text{ "larr" balanced equation}}$

But $a x - a x = 0$

$0 + r = 7 - a x$

$r = 7 - a x$