# How do you solve for x in a(x-2)=b(4-x)?

Mar 20, 2016

We first get rid of the parentheses:

#### Explanation:

$\to a x - 2 a = 4 b - b x$

Then all $x$'s to one side by adding $b x$ to both sides:
$\to a x + b x - 2 a = 4 b - \cancel{b x} + \cancel{b x}$

Then add $2 a$ to both sides to keep only $x$'s on the left:
$\to a x + b x - \cancel{2 a} + \cancel{2 a} = 2 a + 4 b$

Get the $x$'s together:
$\to \left(a + b\right) x = 2 a + 4 b$

Now divide by $a + b$:
$\to x = \frac{2 a + 4 b}{a + b} \mathmr{and} 2 \times \frac{a + 2 b}{a + b}$