# How do you solve for x in ax+b=0?

Mar 12, 2016

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

#### Explanation:

Given:$\text{ } \textcolor{b r o w n}{a x + b = 0}$

Subtract $\textcolor{b l u e}{b}$ from both sides

$\text{ } \textcolor{b r o w n}{a x + b \textcolor{b l u e}{- b} = 0 \textcolor{b l u e}{- b}}$

$\text{ } a x + 0 = - b$

$\text{ } \textcolor{b r o w n}{a x = - b}$

Divide both sides by $\textcolor{b l u e}{a}$ giving

" "color(brown)(a/(color(blue)(a))xxx=-b/(color(blue)(a))

But $\frac{a}{a} = 1$

$\text{ } \textcolor{g r e e n}{x = - \frac{b}{a}}$