To determine which equation has a solution different from the rest, we'll solve each equation.
-
Equation 1:
\(-17x - 34 = 14\)
Adding 34 to both sides:
\(-17x = 48\)
Dividing by -17:
\(x = -\frac{48}{17}\) -
Equation 2:
\(-\frac{1}{7}x - \frac{3}{4} = \frac{1}{4}\)
Adding \(\frac{3}{4}\) to both sides:
\(-\frac{1}{7}x = 1\)
Multiplying both sides by -7:
\(x = -7\) -
Equation 3:
\(-0.35x - 0.52 = 1.93\)
Adding 0.52 to both sides:
\(-0.35x = 2.45\)
Dividing by -0.35:
\(x = -7\) (approximately, as \(-\frac{2.45}{0.35} = -7\)) -
Equation 4:
\(12x - 3 = 12\)
Adding 3 to both sides:
\(12x = 15\)
Dividing by 12:
\(x = \frac{15}{12} = \frac{5}{4}\) -
Equation 5:
\(34x + 5 = -14\)
Subtracting 5 from both sides:
\(34x = -19\)
Dividing by 34:
\(x = -\frac{19}{34}\)
Now summarizing the solutions:
- \(x = -\frac{48}{17} \approx -2.82\)
- \(x = -7\)
- \(x = -7\)
- \(x = \frac{5}{4} = 1.25\)
- \(x = -\frac{19}{34} \approx -0.56\)
The unique and different solution is from Equation 4: \(x = \frac{5}{4}\).
Therefore, the equation that has a solution different from the rest is: 12x−3=12.