Let's analyze each equation to determine how many solutions they have.
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5(x + 1) = 25
Simplifying this equation: \[ 5x + 5 = 25 \ 5x = 20 \ x = 4 \] This equation has exactly one solution.
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12 + 3x + 5 = x + 19 + 2x - 2
Simplifying the left side: \[ 3x + 17 = x + 17 + 2x \ 3x + 17 = 3x + 17 \] This is a true statement that holds for all values of \(x\). Thus, this equation has infinitely many solutions.
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4x = 3(x + 4) - 8
Simplifying this equation: \[ 4x = 3x + 12 - 8 \ 4x = 3x + 4 \ 4x - 3x = 4 \ x = 4 \] This equation has exactly one solution.
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2x + 10 + 6x = 8x - 7
Simplifying this: \[ 8x + 10 = 8x - 7 \ 10 = -7 \] This is a false statement, indicating that there are no solutions.
To summarize:
- 5(x + 1) = 25 → Exactly one solution
- 12 + 3x + 5 = x + 19 + 2x - 2 → Infinitely many solutions
- 4x = 3(x + 4) - 8 → Exactly one solution
- 2x + 10 + 6x = 8x - 7 → No solution
Final placement:
- Exactly one solution: 5(x + 1) = 25, 4x = 3(x + 4) - 8
- Infinitely many solutions: 12 + 3x + 5 = x + 19 + 2x - 2
- No solution: 2x + 10 + 6x = 8x - 7