Bot GPT 4-o mini To determine which of the given equations has a solution different from the others, we will solve each equation one by one.
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Equation 1: \[ \frac{1}{2}x - 3 = \frac{1}{2} \] Adding 3 to both sides: \[ \frac{1}{2}x = \frac{1}{2} + 3 \implies \frac{1}{2}x = \frac{1}{2} + \frac{6}{2} = \frac{7}{2} \] Multiplying both sides by 2: \[ x = 7 \]
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Equation 2: \[ -0.35x - 0.52 = 1.93 \] Adding 0.52 to both sides: \[ -0.35x = 1.93 + 0.52 \implies -0.35x = 2.45 \] Dividing by -0.35: \[ x = \frac{2.45}{-0.35} \approx -7 \]
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Equation 3: \[ -\frac{1}{7}x - \frac{3}{4} = \frac{1}{4} \] Adding \(\frac{3}{4}\) to both sides: \[ -\frac{1}{7}x = \frac{1}{4} + \frac{3}{4} \implies -\frac{1}{7}x = 1 \] Multiplying by -7: \[ x = -7 \]
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Equation 4: \[ \frac{3}{4}x + 5 = -\frac{1}{4} \] Subtracting 5 from both sides: \[ \frac{3}{4}x = -\frac{1}{4} - 5 \implies \frac{3}{4}x = -\frac{1}{4} - \frac{20}{4} = -\frac{21}{4} \] Multiplying by \(\frac{4}{3}\): \[ x = -\frac{21}{4} \cdot \frac{4}{3} = -\frac{21}{3} = -7 \]
Now, summarizing the solutions:
- Equation 1: \(x = 7\)
- Equation 2: \(x \approx -7\)
- Equation 3: \(x = -7\)
- Equation 4: \(x = -7\)
The only equation that has a solution different from the others is Equation 1, which has a solution of \(x = 7\), while the rest have solutions of \(x \approx -7\).
Thus, the answer is: 1/2x−3=1/2.
1 answer