Let's analyze each equation step by step to classify them.
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Equation: \(-4x + 4x = 0\)
Simplification: \[0 = 0\]
Classification: Infinitely Many Solutions (since both sides are equal for any value of \(x\)).
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Equation: \(-x = 7x - 8x\)
Simplification: \[-x = -x\]
Classification: Infinitely Many Solutions.
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Equation: \(5 - x = -x\)
Simplification: \[5 = -x + x\] \[5 = 0\]
Classification: No Solution (since 5 cannot equal 0).
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Equation: \(x + 4 = x + 3\)
Simplification: \[x - x + 4 = 3\] \[4 = 3\]
Classification: No Solution (since 4 cannot equal 3).
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Equation: \(9 = 3(5x - 2)\)
Simplification: \[9 = 15x - 6\] \[15 = 15x\] \[x = 1\]
Classification: One Solution (\(x = 1\)).
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Equation: \(6x - (3x + 8) = 16\)
Simplification: \[6x - 3x - 8 = 16\] \[3x - 8 = 16\] \[3x = 24\] \[x = 8\]
Classification: One Solution (\(x = 8\)).
Summary of Classifications:
- Infinitely Many Solutions
- Infinitely Many Solutions
- No Solution
- No Solution
- One Solution
- One Solution
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