# How do you solve 5+ x + 7x = - 3?

Apr 27, 2018

See a solution process below:

#### Explanation:

First, combine like terms on the left side of the equation:

$5 + x + 7 x = - 3$

$5 + 1 x + 7 x = - 3$

$5 + \left(1 + 7\right) x = - 3$

$5 + 8 x = - 3$

Next, subtract $\textcolor{red}{5}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$5 - \textcolor{red}{5} + 8 x = - 3 - \textcolor{red}{5}$

$0 + 8 x = - 8$

$8 x = - 8$

Now, divide each side of the equation by $\textcolor{red}{8}$ to solve for $x$ while keeping the equation balanced:

$\frac{8 x}{\textcolor{red}{8}} = - \frac{8}{\textcolor{red}{8}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} x}{\cancel{\textcolor{red}{8}}} = - 1$

$x = - 1$

Apr 27, 2018

$x = - 1$

#### Explanation:

Transposing the terms and adding like terms gives us,

$x + 7 x = - 3 - 5$

$8 x = - 8$

$x = - 1$

Apr 27, 2018

$x = - 1$

#### Explanation:

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

$\Rightarrow 5 + 8 x = - 3$

$\text{subtract "5" from both sides}$

$\cancel{5} \cancel{- 5} + 8 x = - 3 - 5$

$\Rightarrow 8 x = - 8$

$\text{divide both sides by } 8$

$\frac{\cancel{8} x}{\cancel{8}} = \frac{- 8}{8}$

$\Rightarrow x = - 1$

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

Substitute this value into the left side of the equation and if equal to the right side then it is the solution.

$5 - 1 - 7 = - 3 = \text{ right side}$

$\Rightarrow x = - 1 \text{ is the solution}$