# How do you solve 3( \frac { 5} { 6} - 2k ) + \frac { 5} { 2} ( 3k - 2) = 8?

Apr 15, 2018

$k = 7$

#### Explanation:

$3 \left(\frac{5}{6} - 2 k\right) + \frac{5}{2} \left(3 k - 2\right) = 8$

$\frac{15}{6} - 6 k + \frac{15}{2} \cdot k - \frac{10}{2} = 8$

$\frac{15}{6} - 6 k + \frac{15}{2} \cdot k - 5 = 8$ multiply both sides by $6$

$6 \cdot \frac{15}{6} - 6 \cdot 6 k + 6 \cdot \frac{15}{2} \cdot k - 6 \cdot 5 = 6 \cdot 8$

$\cancel{\textcolor{red}{6}} \cdot \frac{15}{\cancel{\textcolor{red}{6}}} - 6 \cdot 6 k + \textcolor{g r e e n}{3} \cancel{\textcolor{red}{6}} \cdot \frac{15}{\cancel{\textcolor{red}{2}}} \cdot k - 6 \cdot 5 = 6 \cdot 8$

$15 - 36 k + 45 k - 30 = 48$

$- 36 k + 45 k = 48 + 30 - 15$

$9 k = 63$ divide both sides by $9$

$\frac{9 k}{9} = \frac{63}{9}$

$\frac{\textcolor{red}{\cancel{9}} k}{\textcolor{red}{9}} = 7$

$k = 7$