# How do you solve 7x + 4 = 3x + 7?

Apr 9, 2018

$x = \frac{3}{4}$

#### Explanation:

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

$\text{subtract 3x from both sides}$

$7 x - 3 x + 4 = \cancel{3 x} \cancel{- 3 x} + 7$

$\Rightarrow 4 x + 4 = 7$

$\text{subtract 4 from both sides}$

$4 x \cancel{+ 4} \cancel{- 4} = 7 - 4$

$\Rightarrow 4 x = 3$

$\text{divide both sides by 4}$

$\frac{\cancel{4} x}{\cancel{4}} = \frac{3}{4}$

$\Rightarrow x = \frac{3}{4}$

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

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

$\text{left } = \frac{21}{4} + \frac{16}{4} = \frac{37}{4}$

$\text{right } = \frac{9}{4} + \frac{28}{4} = \frac{37}{5}$

$\Rightarrow x = \frac{3}{4} \text{ is the solution}$