Let's analyze each equation one by one to determine the number of solutions:
A. \( x - 7 = 7 - x \)
Combine like terms:
\[ x + x = 7 + 7 \]
\[ 2x = 14 \]
\[ x = 7 \]
This equation has **one solution**.
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B. \( 3(x + 5) = 3x + 5 \)
Expand the left side:
\[ 3x + 15 = 3x + 5 \]
Subtract \( 3x \) from both sides:
\[ 15 = 5 \]
This is a false statement, indicating that there is no solution. So this equation has **no solutions**.
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C. \( 10 - x = 25 \)
Rearranging gives:
\[ -x = 25 - 10 \]
\[ -x = 15 \]
\[ x = -15 \]
This equation has **one solution**.
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D. \( 2(x + 4) = 2x + 5 + 3 \)
Expand the left side:
\[ 2x + 8 = 2x + 8 \]
Subtract \( 2x \) from both sides:
\[ 8 = 8 \]
This is a true statement for all values of \( x \). Therefore, this equation has **infinitely many solutions**.
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To summarize:
- **: One solution
- **B**: No solutions
- **C**: One solution
- **D**: Infinitely many solutions