Answer
$k= -\displaystyle \frac{3}{8}$
Work Step by Step
The aim is, step by step, to isolate $k$ on one side of the equation.
By multiplying both sides with the LCD of all the fractions, we obtain an equation with no fractions:
(LCD=24)
$\displaystyle \frac{2}{3}k- k+\displaystyle \frac{3}{8}=\frac{1}{2}\qquad.../\times 24$
$ 24\displaystyle \cdot\frac{2}{3}k-24\cdot k+24\displaystyle \cdot\frac{3}{8}=24\cdot\frac{1}{2}\qquad $simplify
$16k-24k+9=12$
Subtract $9$ from both sides and the left side will contain only$ k^{\prime}s.$
$ 16k-24k=12-9 \qquad$... simplify
$-8k=3$
Dividing both sides with $(-8)$ isolates k on the left side.
$-8k=3 \qquad$...$/\div(-8)$
$k= -\displaystyle \frac{3}{8}$
