# How do you solve 8k - 3( k - 5) = 45?

Aug 31, 2017

See a solution process below:

#### Explanation:

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

$8 k - \textcolor{red}{3} \left(k - 5\right) = 45$

$8 k - \left(\textcolor{red}{3} \times k\right) - \left(\textcolor{red}{3} \times - 5\right) = 45$

$8 k - 3 k - \left(- 15\right) = 45$

$8 k - 3 k + 15 = 45$

$\left(8 - 3\right) k + 15 = 45$

$5 k + 15 = 45$

Next, subtract $\textcolor{red}{15}$ from each side of the equation to isolate the $k$ term while keeping the equation balanced:

$5 k + 15 - \textcolor{red}{15} = 45 - \textcolor{red}{15}$

$5 k + 0 = 30$

$5 k = 30$

Now, divide each side of the equation by $\textcolor{red}{5}$ to solve for $k$ while keeping the equation balanced:

$\frac{5 k}{\textcolor{red}{5}} = \frac{30}{\textcolor{red}{5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} k}{\cancel{\textcolor{red}{5}}} = 6$

$k = 6$