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Question

# Evaluate each expression if $p=-4, q=8$, and $r=-10$. See the mentioned example.$\dfrac{-(p+2)^2-3 r}{2-q}$

Solution

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Given that $p=-4$, $q=8$, and $r=-10$, we can evaluate the expression $-\frac{-(p+2)^2-3r}{2-q}$ as follows:

\begin{aligned} \frac{-(p+2)^2-3r}{2-q}&=\frac{-(-4+2)^2-3(-10)}{2-8} &&\text{Substitute p= - 4, q= 8, and r= -10}\\ &=\frac{-(-2)^2-3(-10)}{2-8} &&\text{Add terms inside parentheses}\\ &=\frac{-(4)-3(-10)}{2-8} &&\text{Evaluate the exponential}\\ &=\frac{-4+30}{2-8} &&\text{Simplify}\\ &=\frac{26}{-6} &&\text{Add/Subtract}\\ &=-\frac{13}{3} &&\text{Simplify}\\ \end{aligned}

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