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 others, we need to solve each equation and find their respective solutions.

1. Equation 1: \(-17x - 34 = 14\)

   \(-17x = 14 + 34\)
   \(-17x = 48\)
   \(x = \frac{48}{-17}\)
   \(x = -\frac{48}{17}\)

2. Equation 2: \(-\frac{1}{7}x - \frac{3}{4} = \frac{1}{4}\)

   \(-\frac{1}{7}x = \frac{1}{4} + \frac{3}{4}\)
   \(-\frac{1}{7}x = 1\)
   \(x = -7\)

3. Equation 3: \(-0.35x - 0.52 = 1.93\)

   \(-0.35x = 1.93 + 0.52\)
   \(-0.35x = 2.45\)
   \(x = \frac{2.45}{-0.35}\)
   \(x = -7\)

4. Equation 4: \(12x - 3 = 12\)

   \(12x = 12 + 3\)
   \(12x = 15\)
   \(x = \frac{15}{12}\)
   \(x = \frac{5}{4}\)

5. Equation 5: \(34x + 5 = -14\)

   \(34x = -14 - 5\)
   \(34x = -19\)
   \(x = \frac{-19}{34}\)

Now, let's summarize the solutions:

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

From this analysis, we see:

• Equations 2 and 3 both have the solution \(x = -7\).
• Equation 4 has a unique solution \(x = \frac{5}{4}\).
• Equations 1 and 5 yield different unique results.

However, the distinct solution can be identified among the options. Based on the values computed:

• Equation 4's solution \(x = \frac{5}{4}\) is different from the others.

Therefore, the equation with a solution different from the rest is: 12x − 3 = 12.