# How do you solve for x: 7+ a x = 14- bx?

Apr 15, 2018

$x = \setminus \frac{7}{a + b}$

#### Explanation:

We have:

$7 + a x = 14 - b x$

Isolate all the terms that contain $x$ as a factor on the right hand side and move all the other terms to the left hand side:

$7 + a x = 14 - b x \setminus \implies 7 + a x + b x = 14$

$\setminus \implies a x + b x = 14 - 7 = 7$

Then, use the common factor $x$ to group the terms:

$x \left(a + b\right) = 7 \setminus \implies x = \setminus \frac{7}{a + b}$

Note that this assumes that $a + b \setminus \ne 0$.