# How do you solve  5x - 3 = 13 - 3x ?

May 29, 2018

$x = 2$

#### Explanation:

$\text{collect terms in x on the left side of the equation and}$
$\text{numeric values on the right side}$

$\text{add "3x" to both sides}$

$5 x + 3 x - 3 = 13 \cancel{- 3 x} \cancel{+ 3 x}$

$8 x - 3 = 13$

$\text{add 3 to both sides}$

$8 x \cancel{- 3} \cancel{+ 3} = 13 + 3$

$8 x = 16$

$\text{divide both sides by 8}$

$\frac{\cancel{8} x}{\cancel{8}} = \frac{16}{8} \Rightarrow x = 2$

$\textcolor{b l u e}{\text{As a check}}$

Substitute this value into the equation and if both sides are equal then it is the solution.

$\text{left } = \left(5 \times 2\right) - 3 = 10 - 3 = 7$

$\text{right } = 13 - \left(3 \times 2\right) = 13 - 6 = 7$

$x = 2 \text{ is the solution}$