# How do you solve 1/2(4x-6)=11 using the distributive property?

Jun 27, 2017

See a solution process below:

#### Explanation:

First, expand the term in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{\frac{1}{2}} \left(4 x - 6\right) = 11$

$\left(\textcolor{red}{\frac{1}{2}} \times 4 x\right) - \left(\textcolor{red}{\frac{1}{2}} \times 6\right) = 11$

$\frac{4}{2} x - \frac{6}{2} = 11$

$2 x - 3 = 11$

Next, add $\textcolor{red}{3}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$2 x - 3 + \textcolor{red}{3} = 11 + \textcolor{red}{3}$

$2 x - 0 = 14$

$2 x = 14$

Now, divide each side of the equation by $\textcolor{red}{2}$ to solve for $x$ while keeping the equation balanced:

$\frac{2 x}{\textcolor{red}{2}} = \frac{14}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} = 7$

$x = 7$