How do you solve -6( - 7x - 6) = 8x + 36?

May 21, 2017

See a solution process below:

Explanation:

First, expand the term in parenthesis on the left side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{- 6} \left(- 7 x - 6\right) = 8 x + 36$

$\left(\textcolor{red}{- 6} \cdot - 7 x\right) + \left(\textcolor{red}{- 6} \cdot - 6\right) = 8 x + 36$

$42 x + 36 = 8 x + 36$

Next, subtract $\textcolor{red}{36}$ and $\textcolor{b l u e}{8 x}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$- \textcolor{b l u e}{8 x} + 42 x + 36 - \textcolor{red}{36} = - \textcolor{b l u e}{8 x} + 8 x + 36 - \textcolor{red}{36}$

$\left(- \textcolor{b l u e}{8} + 42\right) x + 0 = 0 + 0$

$34 x = 0$

Now, divide each side of the equation by $\textcolor{red}{34}$ to solve for $x$ while keeping the equation balanced:

$\frac{34 x}{\textcolor{red}{34}} = \frac{0}{\textcolor{red}{34}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{34}}} x}{\cancel{\textcolor{red}{34}}} = 0$

$x = 0$