# How do you solve \frac { 3x + 15+ ( 11x - 5) } { 2} = 47?

Mar 14, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{2}$ to eliminate the fraction and keep the equation balanced:

$\textcolor{red}{2} \times \frac{3 x + 15 + \left(11 x - 5\right)}{2} = \textcolor{red}{2} \times 47$

$\cancel{\textcolor{red}{2}} \times \frac{3 x + 15 + \left(11 x - 5\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} = 94$

$3 x + 15 + \left(11 x - 5\right) = 94$

Next, remove the terms on the left hand side of the equation from parenthesis, group and combine like terms:

$3 x + 15 + 11 x - 5 = 94$

$3 x + 11 x + 15 - 5 = 94$

$\left(3 + 11\right) x + \left(15 - 5\right) = 94$

$14 x + 10 = 94$

Then, subtract $\textcolor{red}{10}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$14 x + 10 - \textcolor{red}{10} = 94 - \textcolor{red}{10}$

$14 x + 0 = 84$

$14 x = 84$

Now, divide each side of the equation by $\textcolor{red}{14}$ to solve for $x$ while keeping the equation balanced:

$\frac{14 x}{\textcolor{red}{14}} = \frac{84}{\textcolor{red}{14}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{14}}} x}{\cancel{\textcolor{red}{14}}} = 6$

$x = 6$