Multiply the reciprocals of $\frac{-5}{2},\frac{4}{35}$ and add the additive inverse of $\frac{3}{2}$ to the product. Find the result.

The correct option is C $-5$
The reciprocal of $\frac{-5}{2}=\frac{-2}{5}$

The reciprocal of $\frac{4}{35}=\frac{35}{4}$

Product of the reciprocals
$=\frac{-2}{5}\times \frac{35}{4}=\frac{-7}{2}$

The additive inverse of $\left(\frac{3}{2}\right)$ is $\frac{-3}{2}$.

Thus Product + the additive inverse $\frac{(-7)}{2}+\frac{(-3)}{2}=\frac{-7-3}{2}=\frac{-10}{2}=(-5).$