Which of the following equations has a solution different from the rest? (1 point)

Question

Responses

−17x−34=14
negative Start Fraction 1 over 7 End Fraction x minus Start Fraction 3 over 4 End Fraction equals Start Fraction 1 over 4 End Fraction

−0.35x−0.52=1.93
negative 0.35 x minus 0.52 equals 1.93

12x−3=12
Start Fraction 1 over 2 End Fraction x minus 3 equals Start Fraction 1 over 2 End Fraction

34x+5=−14

Answer 1

To determine which equation has a solution different from the rest, we'll solve each equation.

1. Equation 1:
   \(-17x - 34 = 14\)
   Adding 34 to both sides:
   \(-17x = 48\)
   Dividing by -17:
   \(x = -\frac{48}{17}\)

2. 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:
   \(x = -7\)

3. 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 \(-\frac{2.45}{0.35} = -7\))

4. Equation 4:
   \(12x - 3 = 12\)
   Adding 3 to both sides:
   \(12x = 15\)
   Dividing by 12:
   \(x = \frac{15}{12} = \frac{5}{4}\)

5. Equation 5:
   \(34x + 5 = -14\)
   Subtracting 5 from both sides:
   \(34x = -19\)
   Dividing by 34:
   \(x = -\frac{19}{34}\)

Now summarizing the solutions:

1. \(x = -\frac{48}{17} \approx -2.82\)
2. \(x = -7\)
3. \(x = -7\)
4. \(x = \frac{5}{4} = 1.25\)
5. \(x = -\frac{19}{34} \approx -0.56\)

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.