Asked by IGotYa
Which of the following equations has exactly one solution? a. −3x+8=−3x−8 b. 3x−8=3x+8 c. −3x−8=3x−8 d. −8x+3=−8x+3
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GPT-5 mini
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c. −3x−8 = 3x−8
Reason: If the x-coefficients are different the equation has exactly one solution. In (c) −3 ≠ 3, so solve:
−3x − 8 = 3x − 8 → add 3x: −8 = 6x − 8 → add 8: 0 = 6x → x = 0.
For the others: (a) and (b) have same x-coefficients but different constants → no solution; (d) is identical on both sides → infinitely many solutions.
Reason: If the x-coefficients are different the equation has exactly one solution. In (c) −3 ≠ 3, so solve:
−3x − 8 = 3x − 8 → add 3x: −8 = 6x − 8 → add 8: 0 = 6x → x = 0.
For the others: (a) and (b) have same x-coefficients but different constants → no solution; (d) is identical on both sides → infinitely many solutions.
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