Beginning Algebra With Applications, Chapter 3, 3.3, Section 3.3, Problem 138

Evaluate $\displaystyle \frac{1}{4}(8 - 12d) < \frac{2}{5}(10d + 15)$

$
\begin{equation}
\begin{aligned}
\frac{1}{4} (8) - \frac{1}{4} (12d) &< \frac{2}{5} (10d) + \frac{2}{5}(15)&& \text{Use the Distributive Property to remove the parenthesis}\\
\\
2 - 3d &< 4d + 6 && \text{Simplify}\\
\\
-3d -4 d &< 6 - 2 && \text{Group terms}\\
\\
-7d &< 4 && \text{Combine like terms}\\
\\
\frac{-7d}{-7} &< \frac{4}{-7} && \text{Divide each side by -7}\\
\\
d &> -\frac{4}{7} && \text{Remember that if you divide or multiply numbers ,the inequality symbol reverses}
\end{aligned}
\end{equation}
$

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