Beginning Algebra With Applications, Chapter 3, 3.3, Section 3.3, Problem 140

Evaluate $\displaystyle \frac{3}{8}(16 - 8c) - 9 \geq \frac{3}{5}(10c - 15) + 7$

$
\begin{equation}
\begin{aligned}
\frac{3}{8} (16) - \frac{3}{8} (8c) - 9 &\geq \frac{3}{5}(10c) - \frac{3}{5} (15) + 7 && \text{Use the Distributive Property to remove the parenthesis}\\
\\
6 - 3c - 9 &\geq 6c - 9 + 7 && \text{Simplify}\\
\\
-3c - 6c &\geq - 9 + 7 - 6 + 9 && \text{Group terms}\\
\\
-9c &\geq 1 && \text{Combine like terms}\\
\\
\frac{-9c}{-9} &\geq \frac{1}{-9} && \text{Divide each side by -9}\\
\\
c &\leq -\frac{1}{9} && \text{Remember that if you divide or multiply numbers ,the inequality symbol reverses}
\end{aligned}
\end{equation}
$

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