How do you solve -15x - 40= 9- 8x?

Feb 28, 2017

$\textcolor{g r e e n}{x = 7}$

Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} - 15 x - 40 = 9 - 8 x$

Add $8 x + 40 \left(= 40 + 8 x\right)$ to both sides in order to isolate the variable term on the left and the constant term on the right:
$\textcolor{w h i t e}{\text{XXX")-15x-40=color(white)("x}} 9 - 8 x$
$\textcolor{w h i t e}{\text{XXX")+color(white)("x}} \underline{8 x + 40} = \underline{40 + 8 x}$
$\textcolor{w h i t e}{\text{XXXX")-7xcolor(white)("xxxx}} = 49$

Divide both sides by $\left(- 7\right)$
$\textcolor{w h i t e}{\text{XXXXXX")xcolor(white)("xxxx}} = 7$

Feb 28, 2017

See the entire solution process below:

Explanation:

First, add $\textcolor{red}{15 x}$ and subtract $\textcolor{b l u e}{9}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$- 15 x - 40 + \textcolor{red}{15 x} - \textcolor{b l u e}{9} = 9 - 8 x + \textcolor{red}{15 x} - \textcolor{b l u e}{9}$

$- 15 x + \textcolor{red}{15 x} - 40 - \textcolor{b l u e}{9} = 9 - \textcolor{b l u e}{9} - 8 x + \textcolor{red}{15 x}$

$0 - 49 = 0 + 7 x$

$- 49 = 7 x$

Now, divide each side of the equation by $\textcolor{red}{7}$ to solve for $x$ while keeping the equation balanced:

$- \frac{49}{\textcolor{red}{7}} = \frac{7 x}{\textcolor{red}{7}}$

$- 7 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} x}{\cancel{\textcolor{red}{7}}}$

$- 7 = x$

$x = - 7$