Question
\begin{tabular}{l} 4) Which expression is equivalent to \( 10 c-6 c+3+7 d+12+4 d 7 \) \\ \( 7 c+11 d+12 \square 4 c+11 d+16] 16 c+11 d+15 \square 1 c+10 d+16 \) \\ \hline\end{tabular}
Ask by Harris Long. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \(4c + 11d + 15\).
Solution
1. Start with the expression
\(10c - 6c + 3 + 7d + 12 + 4d\).
2. Combine the like terms for \(c\):
\(10c - 6c = 4c\).
3. Combine the like terms for \(d\):
\(7d + 4d = 11d\).
4. Combine the constant terms:
\(3 + 12 = 15\).
5. Thus, the simplified expression is
\[
4c + 11d + 15.
\]
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Simplify this solution Extra Insights
To solve the expression \( 10c - 6c + 3 + 7d + 12 + 4d \), we first combine like terms. - For \(c\), we have \(10c - 6c = 4c\). - For \(d\), we have \(7d + 4d = 11d\). - The constant terms are \(3 + 12 = 15\). Thus, the simplified expression is \(4c + 11d + 15\). Now let's compare this with the options provided: - \(7c + 11d + 12\) - \(4c + 11d + 16\) - \(16c + 11d + 15\) - \(1c + 10d + 16\) None of the first options match our simplified expression. The closest one is \(4c + 11d + 16\), but it has a different constant term. Therefore, none of the given options are equivalent to \(10c - 6c + 3 + 7d + 12 + 4d\).
