# How do you solve 1/2k-3=2-3/4k ?

Apr 23, 2018

$k = 4$

#### Explanation:

Given: $\frac{1}{2} k - 3 = 2 - \frac{3}{4} k$.

Add $3$ to both sides.

$\implies \frac{1}{2} k - \textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} = 2 - \frac{3}{4} k + 3$

$\implies \frac{1}{2} k = 5 - \frac{3}{4} k$

Add $\frac{3}{4} k$ from both sides.

$\implies \frac{1}{2} k + \frac{3}{4} k = 5 + \textcolor{red}{\cancel{\textcolor{b l a c k}{\frac{3}{4} k}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{\frac{3}{4} k}}}$

$\implies \frac{2}{4} k + \frac{3}{4} k = 5$

$\implies \frac{5}{4} k = 5$

Multiply by $\frac{4}{5}$ on both sides.

$\implies \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}} k \cdot \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}} = 5 \cdot \frac{4}{5}$

$\implies k = 4$