Intermediate Algebra, Chapter 1, 1.3, Section 1.3, Problem 78

Simplify $\displaystyle \frac{\displaystyle -4 \left( \frac{12 - (-8)}{3 \cdot 2 + 4} \right) - 5 (-1-7) }{-9- (-7) - [-5-(-8)]}$ using the Order of Operations.


$
\begin{equation}
\begin{aligned}

\frac{\displaystyle -4 \left( \frac{12 - (-8)}{3 \cdot 2 + 4} \right) - 5 (-1-7) }{-9- (-7) - [-5-(-8)]} =& \frac{\displaystyle -4 \left( \frac{12-(-8)}{6+4} \right) -5(-1-7) }{-9-(-7) - [3]}
&& \text{Work separately above and below the fraction bar}
\\
\\
=& \frac{\displaystyle -4 \left( \frac{20}{10} \right) - 5(-8) }{-9-(-7) - 3}
&& \text{Work inside parentheses first}
\\
\\
=& \frac{-8 - 5 (-8)}{-9-(-7) - 3}
&& \text{Multiply}
\\
\\
=& \frac{-8 + 40}{-9 - (-7) - 3}
&& \text{Multiply}
\\
\\
=& \frac{32}{-2-3}
&& \text{Work separately above and below the fraction bar}
\\
\\
=& \frac{32}{-5}
&& \text{Subtract}
\\
\\
=& \frac{-32}{5}


\end{aligned}
\end{equation}
$