Answer
$\dfrac{5}{6}x+\dfrac{15}{4}$
Work Step by Step
The Distributive Property states that for any real numbers $a, b$, and $c$:
$$a(b+c)=ab+ac$$
Apply the Distributive Property to obtain:
$$\begin{align*}
\frac{5}{6}\left(x+\frac{1}{2}+4\right)&=\frac{5}{6}(x)+\frac{5}{6}\cdot \frac{1}{2}+\frac{5}{6}\cdot4\\
&=\frac{5}{6}x+\frac{5}{12}+\frac{20}{6}\\
\end{align*}$$
Make the last two fractions similar using their LCD which is $12$:
$$
\require{cancel}
\begin{align*}
\frac{5}{6}x+\frac{5}{12}+\frac{20}{6}&=\frac{5}{6}x+\frac{5}{12}+\frac{40}{12}\\
&=\frac{5}{6}x+\frac{45}{12}\\
&=\frac{5}{6}x+\frac{15(3)}{4(3)}\\
&=\frac{5}{6}x+\frac{15\cancel{(3)}}{4\cancel{(3)}}\\
&=\frac{5}{6}x+\frac{15}{4}\\
\end{align*}$$
