Intermediate Algebra, Chapter 1, 1.3, Section 1.3, Problem 94

Evaluate the expression $\displaystyle \frac{7y - 5x}{2w}$ for $\displaystyle w = 4, x = - \frac{3}{4}$ and $z = 1.25$.


$
\begin{equation}
\begin{aligned}

\frac{7y - 5x}{2w} =& \frac{\displaystyle 7 \left( \frac{1}{2} \right) - 5 \left( - \frac{3}{4} \right) }{2(4)}
&& \text{Substitute } w = 4, x = - \frac{3}{4} \text{ and } y = \frac{1}{2}
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=& \frac{\displaystyle \frac{7}{2} - 5 \left( - \frac{3}{4} \right) }{8}
&& \text{Work separately above and below the fraction bar}
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=& \frac{\displaystyle \frac{7}{2} + \frac{15}{4}}{8}
&& \text{Multiply}
\\
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=& \frac{\displaystyle \frac{14}{4} + \frac{15}{4}}{8}
&& \text{Get the LCD}
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=& \frac{\displaystyle \frac{29}{4}}{8}
&& \text{Add}
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=& \frac{29}{4} \cdot \frac{1}{8}
&& \text{Get the reciprocal}
\\
\\
=& \frac{29}{32}
&& \text{Multiply}

\end{aligned}
\end{equation}
$