To find which equation has a solution different from the rest, let's solve each equation one by one.
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Equation 1: \(-17x - 34 = 14\)
Adding \(34\) to both sides: \(-17x = 14 + 34\) \(-17x = 48\)
Dividing by \(-17\): \(x = -\frac{48}{17}\)
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Equation 2: \(\frac{1}{7}x - \frac{3}{4} = \frac{1}{4}\)
Adding \(\frac{3}{4}\) to both sides: \(\frac{1}{7}x = \frac{1}{4} + \frac{3}{4}\) \(\frac{1}{7}x = 1\)
Multiplying both sides by \(7\): \(x = 7\)
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Equation 3: \(12x - 3 = 12\)
Adding \(3\) to both sides: \(12x = 12 + 3\) \(12x = 15\)
Dividing by \(12\): \(x = \frac{15}{12} = \frac{5}{4}\)
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Equation 4: \(\frac{1}{2}x - 3 = \frac{1}{2}\)
Adding \(3\) to both sides: \(\frac{1}{2}x = \frac{1}{2} + 3\) \(\frac{1}{2}x = \frac{1}{2} + \frac{6}{2} = \frac{7}{2}\)
Multiplying by \(2\): \(x = 7\)
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Equation 5: \(34x + 5 = -14\)
Subtracting \(5\) from both sides: \(34x = -14 - 5\) \(34x = -19\)
Dividing by \(34\): \(x = -\frac{19}{34}\)
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Equation 6: \(-0.35x - 0.52 = 1.93\)
Adding \(0.52\) to both sides: \(-0.35x = 1.93 + 0.52\) \(-0.35x = 2.45\)
Dividing by \(-0.35\): \(x = \frac{-2.45}{0.35} = -7\)
Now let's summarize the solutions:
- Equation 1: \(x = -\frac{48}{17}\)
- Equation 2: \(x = 7\)
- Equation 3: \(x = \frac{5}{4}\)
- Equation 4: \(x = 7\)
- Equation 5: \(x = -\frac{19}{34}\)
- Equation 6: \(x = -7\)
The solutions for Equations 2 and 4 are both \(x = 7\). Hence, they are the same.
Other solutions are:
- \(-\frac{48}{17} \approx -2.82\)
- \(\frac{5}{4} = 1.25\)
- \(-\frac{19}{34} \approx -0.56\)
- \(-7\)
The solution that stands out is \(x = 7\) for both 2 and 4 while all others are different. Therefore, the unique equation in terms of solution is Equation 3: \(x = \frac{5}{4}\) which has a different solution than the rest.
Thus, the equation with a solution different from the rest is Equation 3: \(12x - 3 = 12\).
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