# How do you solve for b in a = 2b?

##### 1 Answer
Jun 28, 2015

$b = \frac{1}{2} a$

#### Explanation:

As long as you perform the same arithmetic operation on both sides of an equation (exception: other than attempting to divide by zero) the equation remains valid.

If $a = 2 b$
then we can divide both sides by 2
$\textcolor{w h i t e}{\text{XXXX}}$$\frac{a}{2} = \frac{\cancel{2} b}{\cancel{2}}$
$\frac{a}{2}$ can be written $\frac{1}{2} a$ (personal preference allowed)
$\textcolor{w h i t e}{\text{XXXX}}$$\frac{1}{2} a = b$

Or, since an equality is reflexive:
$\textcolor{w h i t e}{\text{XXXX}}$$b = \frac{1}{2} a$