Question
Solve the following equation using the addition property of equality. \( \begin{array}{l}9 p+7=8 p+10\end{array} \) The solution set is \( \{\square\} \).
Ask by Chandler Marshall. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution is \( p = 3 \).
Solution
1. Start with the equation:
\[
9p + 7 = 8p + 10
\]
2. Subtract \(8p\) from both sides (using the addition property of equality):
\[
9p - 8p + 7 = 10
\]
which simplifies to:
\[
p + 7 = 10
\]
3. Subtract \(7\) from both sides:
\[
p + 7 - 7 = 10 - 7
\]
which gives:
\[
p = 3
\]
The solution set is \( \{3\} \).
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Simplify this solution Beyond the Answer
To solve the equation \( 9p + 7 = 8p + 10 \), we want to isolate the variable \( p \). First, we can subtract \( 8p \) from both sides to eliminate \( p \) on the right side: \( 9p - 8p + 7 = 10 \) This simplifies to: \( p + 7 = 10 \) Next, we subtract 7 from both sides to isolate \( p \): \( p + 7 - 7 = 10 - 7 \) This gives us: \( p = 3 \) Thus, the solution set is \( \{3\} \).
