# How do you solve for x in C=b-bx?

Apr 27, 2018

$x = 1 - \frac{C}{b}$

#### Explanation:

Let's start by rewriting as

$b x - b = - C$

Now factor

$b \left(x - 1\right) = - C$

$x - 1 = - \frac{C}{b}$

$x = 1 - \frac{C}{b}$

Hopefully this helps!

Apr 27, 2018

$x = 1 - \frac{C}{b}$

#### Explanation:

You can separate the constants from the variable with algebraic operations. In this case we will still end up with an expression in C and b, as they are not given values.

$C = b - b x = b \left(1 - x\right)$ (distributive property)
$\frac{C}{b} = 1 - x$ (divide both sides by b)
$\frac{C}{b} - 1 = - x$ (subtract 1 from both sides)
$x = 1 - \frac{C}{b}$ (multiply both sides by -1 and rearrange for neatness)

NOW, given any C and b, x can be calculated directly.