Asked by izuku midoriya
Which of the following equations has exactly one solution?(1 point) Responses −5x+3=−5x+3 negative 5 x plus 3 equals negative 5 x plus 3 5x+4=5x+4 5 x plus 4 equals 5 x plus 4 5x+4=5x+3 5 x plus 4 equals 5 x plus 3 −5x+4=5x+4
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Answered by
GPT-4o mini
To determine which of the equations has exactly one solution, let's analyze each option:
1. **\-5x + 3 = \-5x + 3**: This equation is true for all values of \( x \). (Infinite solutions)
2. **5x + 4 = 5x + 4**: This equation is also true for all values of \( x \). (Infinite solutions)
3. **5x + 4 = 5x + 3**: Subtracting \( 5x \) from both sides gives \( 4 = 3 \), which is false. (No solutions)
4. **\-5x + 4 = 5x + 4**: Adding \( 5x \) to both sides gives \( 4 = 10x + 4 \). Subtracting \( 4 \) from both sides gives \( 0 = 10x \), leading to \( x = 0 \). (Exactly one solution)
From the analysis above, the equation that has exactly one solution is:
**\-5x + 4 = 5x + 4.**
1. **\-5x + 3 = \-5x + 3**: This equation is true for all values of \( x \). (Infinite solutions)
2. **5x + 4 = 5x + 4**: This equation is also true for all values of \( x \). (Infinite solutions)
3. **5x + 4 = 5x + 3**: Subtracting \( 5x \) from both sides gives \( 4 = 3 \), which is false. (No solutions)
4. **\-5x + 4 = 5x + 4**: Adding \( 5x \) to both sides gives \( 4 = 10x + 4 \). Subtracting \( 4 \) from both sides gives \( 0 = 10x \), leading to \( x = 0 \). (Exactly one solution)
From the analysis above, the equation that has exactly one solution is:
**\-5x + 4 = 5x + 4.**
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