# How do you simplify 2/5 (5k + 35) - 8?

Mar 27, 2018

The simplified expression is $2 k + 6$.

#### Explanation:

Use the distributive property:

$\textcolor{m a \ge n t a}{a} \left(\textcolor{red}{x} + \textcolor{b l u e}{y}\right) = \textcolor{m a \ge n t a}{a} \cdot \textcolor{red}{x} + \textcolor{m a \ge n t a}{a} \cdot \textcolor{b l u e}{y}$

Here's this property applied to our expression:

$\textcolor{w h i t e}{=} \textcolor{m a \ge n t a}{\frac{2}{5}} \left(\textcolor{red}{5 k} + \textcolor{b l u e}{35}\right) - 8$

$= \textcolor{m a \ge n t a}{\frac{2}{5}} \cdot \textcolor{red}{5 k} + \textcolor{m a \ge n t a}{\frac{2}{5}} \cdot \textcolor{b l u e}{35} - 8$

$= \textcolor{m a \ge n t a}{\frac{2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}}} \cdot \textcolor{red}{\textcolor{b l a c k}{\cancel{\textcolor{red}{5}}} k} + \textcolor{m a \ge n t a}{\frac{2}{5}} \cdot \textcolor{b l u e}{35} - 8$

$= \textcolor{m a \ge n t a}{2} \textcolor{red}{k} + \textcolor{m a \ge n t a}{\frac{2}{5}} \cdot \textcolor{b l u e}{35} - 8$

$= \textcolor{m a \ge n t a}{2} \textcolor{red}{k} + \textcolor{m a \ge n t a}{\frac{2 \textcolor{b l a c k}{\cdot} \textcolor{b l u e}{35}}{5}} - 8$

$= \textcolor{m a \ge n t a}{2} \textcolor{red}{k} + \textcolor{m a \ge n t a}{\frac{\textcolor{p u r p \le}{70}}{5}} - 8$

$= \textcolor{m a \ge n t a}{2} \textcolor{red}{k} + \textcolor{p u r p \le}{14} - 8$

$= \textcolor{m a \ge n t a}{2} \textcolor{red}{k} + 6$

That's the expanded expression. Hope this helped!

Mar 27, 2018

2/5(5k+35)-8=color(blue)(2k+6

#### Explanation:

Simplify:

$\frac{2}{5} \left(5 k + 35\right) - 8$

Expand.

$\frac{10 k}{5} + \frac{70}{5} - 8$

Multiply $8$ by $\frac{5}{5}$ to get the least common denominator $5$. Multiplying by $\frac{5}{5}$ is the same as multiplying by $1$, so the numbers will change, but the value of the fraction will stay the same.

$\frac{10 k}{5} + \frac{70}{5} - 8 \times \frac{5}{5}$

Simplify.

$\frac{{\textcolor{red}{\cancel{\textcolor{b l a c k}{10}}}}^{2} k}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}} ^ 1 + {\textcolor{red}{\cancel{\textcolor{b l a c k}{70}}}}^{14} / {\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}}^{1} - {\textcolor{red}{\cancel{\textcolor{b l a c k}{40}}}}^{8} / {\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}}^{1}$

Simplify.

$2 k + 14 - 8$

$2 k + 6$