Answer
$h=\frac{3}{8}$
Work Step by Step
$$\begin{align*}
\frac{1}{2}(6h)-\frac{1}{2}(4)&=-5h+1 &\text{Apply the Distributive Property.}\\
3h-2&=-5h+1 &\text{Simplify.}\\
3h-2+2&=-5h+1+2 &\text{Add $2$ to both sides.}\\
3h&=-5h+3 &\text{Simplify.}\\
3h+5h&=-5h+3+5h &\text{Add $5h$ to both sides.}\\
8h&=3 &\text{Simplify.}\\
\frac{8h}{8}&=\frac{3}{8} &\text{Divide $8$ to both sides.}\\
h&=\frac{3}{8} &\text{Simplify.}
\end{align*}$$
Check if the answer is correct by substituting $\frac{3}{8}$ to the variable in the given equation.
$$\begin{align*}
\frac{1}{2}(6h-4)&=-5h+1\\
\frac{1}{2}\left(6\cdot \frac{3}{8}-4\right)&=-5\cdot \frac{3}{8}+1\\
\frac{1}{2}\left(\frac{-7}{4}\right)&\stackrel{?}{=}\frac{-15}{8}+1\\
\frac{-7}{8}&\stackrel{\checkmark}{=}\frac{-7}{8}
\end{align*}$$
