To determine which of the given equations has exactly one solution, we can analyze each equation:
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Equation: -8x + 3 = -8x + 3
This equation simplifies to 0 = 0, which is true for all values of \( x \). Therefore, it has infinitely many solutions.
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Equation: 3x - 8 = 3x - 8
Similar to the first equation, this simplifies to 0 = 0, which is also true for all values of \( x \). Thus, it has infinitely many solutions.
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Equation: -3x + 8 = 3x - 8
To solve for \( x \): \[ -3x + 8 = 3x - 8 \] Combine like terms: \[ 8 + 8 = 3x + 3x \] \[ 16 = 6x \] Divide by 6: \[ x = \frac{16}{6} = \frac{8}{3} \] This equation has exactly one solution: \( x = \frac{8}{3} \).
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Equation: -3x + 8 = -3x - 8
To solve for \( x \): \[ -3x + 8 = -3x - 8 \] Add \( 3x \) to both sides: \[ 8 = -8 \] This is a contradiction, which means there are no solutions.
Conclusion: The only equation from the list that has exactly one solution is 3. -3x + 8 = 3x - 8.
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