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Which of the following equations has exactly one solution?
A. -5x + 3 = -5x + 3
B. 5x + 4 = 5x + 3
C. -5x + 4 = 5x + 4
D. 5x + 4 = 5x + 4
A. -5x + 3 = -5x + 3
B. 5x + 4 = 5x + 3
C. -5x + 4 = 5x + 4
D. 5x + 4 = 5x + 4
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Answered by
GPT-4o mini
To determine which of the given equations has exactly one solution, let's analyze each option:
A. \(-5x + 3 = -5x + 3\)
This is an identity, meaning it is true for all values of \(x\). Therefore, it has infinitely many solutions.
B. \(5x + 4 = 5x + 3\)
Subtracting \(5x\) from both sides results in \(4 = 3\), which is a false statement. Therefore, there are no solutions.
C. \(-5x + 4 = 5x + 4\)
Rearranging gives \(-5x - 5x = 4 - 4\) or \(-10x = 0\), leading to \(x = 0\). This equation has exactly one solution.
D. \(5x + 4 = 5x + 4\)
Similar to option A, this is also an identity and has infinitely many solutions.
Upon analyzing all equations, the only equation with exactly one solution is:
**C. \(-5x + 4 = 5x + 4**.
A. \(-5x + 3 = -5x + 3\)
This is an identity, meaning it is true for all values of \(x\). Therefore, it has infinitely many solutions.
B. \(5x + 4 = 5x + 3\)
Subtracting \(5x\) from both sides results in \(4 = 3\), which is a false statement. Therefore, there are no solutions.
C. \(-5x + 4 = 5x + 4\)
Rearranging gives \(-5x - 5x = 4 - 4\) or \(-10x = 0\), leading to \(x = 0\). This equation has exactly one solution.
D. \(5x + 4 = 5x + 4\)
Similar to option A, this is also an identity and has infinitely many solutions.
Upon analyzing all equations, the only equation with exactly one solution is:
**C. \(-5x + 4 = 5x + 4**.
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