# How do you solve for x in ax = bx -c?

Jul 27, 2018

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

#### Explanation:

$\text{Collect terms in x on the left side }$

$\text{subtract "bx" from both sides}$

$a x - b x = - c$

$\text{take out a "color(blue)"common factor } x$

$x \left(a - b\right) = - c$

$\text{divide both sides by } a - b$

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

Jul 28, 2018

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

#### Explanation:

If we want to solve for $x$, we can first get all of our $x$ terms on one side. This can easily be done by subtracting $b x$ from both sides.

We now have

$a x - b x = - c$

Since both terms on the left have an $x$ in common, we can factor that out to get

$x \left(a - b\right) = - c$

Lastly, we can divide both sides by $a - b$ to get

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

Hope this helps!