# How do you solve for c in a(b – c) = d?

Mar 23, 2018

$c = b - \frac{d}{a}$

#### Explanation:

Given: $a \left(b - c\right) = d$

Divide by $a$ on both sides.

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{a}}} \left(b - c\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{a}}}} = \frac{d}{a}$

$b - c = \frac{d}{a}$

Subtract $b$ from both sides.

$\textcolor{red}{\cancel{\textcolor{b l a c k}{b}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{b}}} - c = \frac{d}{a} - b$

$- c = \frac{d}{a} - b$

Reverse signs.

$\therefore c = - \left(\frac{d}{a} - b\right)$

$= b - \frac{d}{a}$

Mar 23, 2018

$c = b - \frac{d}{a}$

#### Explanation:

$\text{divide both sides by a}$

$\frac{\cancel{a}}{\cancel{a}} \left(b - c\right) = \frac{d}{a}$

$\Rightarrow b - c = \frac{d}{a}$

$\text{subtract b from both sides}$

$\cancel{b} - \cancel{b} - c = \frac{d}{a} - b$

$\Rightarrow - c = \frac{d}{a} - b$

$\text{multiply all terms on both sides by } - 1$

$\Rightarrow c = - \frac{d}{a} + b$

$\Rightarrow c = b - \frac{d}{a}$