Answer
$\{0.3\}$.
Work Step by Step
Multiply both sides by $2y$.
$2y\left(\dfrac{4}{y}-5\right)=2y\left(\dfrac{5}{2y}\right)$
Use distributive property.
$\begin{align*}
2y\left(\dfrac{4}{y}\right)-2y(5)&=2y\left(\dfrac{5}{2y}\right)\\
2y\cdot\frac{4}{y}-2y\cdot 5&=2y\cdot \frac{5}{2y}
\end{align*}$
Simplify.
$\begin{align*}
\require{cancel}
2\cancel{y}\cdot\frac{4}{\cancel{y}}-2y\cdot 5&=\cancel{2y}\cdot \frac{5}{\cancel{2y}}\\
8-10y&=5
\end{align*}$
Add $10y-5$ to both sides.
$8-10y+10y-5=5+10y-5$
Simplify.
$3=10y$
Divide both sides by $10$.
$\dfrac{3}{10}=\dfrac{10y}{10}$
Simplify.
$0.3=y$
Hence, the solution to the equation is $\{0.3\}$.
