#### Answer

$\dfrac{1}{3}x-\dfrac{13}{2}$

#### Work Step by Step

Without an equal sign, the given is an $\text{
expression
}.$
By combining like terms, the given expression, $
\dfrac{1}{2}x-\dfrac{1}{6}x+\dfrac{3}{2}-8
,$ simplifies to
\begin{array}{l}\require{cancel}
\left( \dfrac{1}{2}x-\dfrac{1}{6}x \right)+\left( \dfrac{3}{2}-8 \right)
\\\\=
\left( \dfrac{3}{6}x-\dfrac{1}{6}x \right)+\left( \dfrac{3}{2}-\dfrac{16}{2} \right)
\\\\=
\left( \dfrac{3-1}{6}x\right)+\left( \dfrac{3-16}{2}\right)
\\\\=
\left( \dfrac{2}{6}x\right)+\left( \dfrac{-13}{2}\right)
\\\\=
\dfrac{1}{3}x-\dfrac{13}{2}
.\end{array}