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

34x+5=−14
Start Fraction 3 over 4 End Fraction x plus 5 equals negative Start Fraction 1 over 4 End Fraction

12x−3=12

Answer 1

To determine which equation has a solution different from the rest, we will solve each equation step by step.

1. Equation 1:
   \(-17x - 34 = 14\)
   \(-17x = 14 + 34\)
   \(-17x = 48\)
   \(x = -\frac{48}{17}\)

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

4. Equation 4:
   \(34x + 5 = -14\)
   \(34x = -14 - 5\)
   \(34x = -19\)
   \(x = -\frac{19}{34}\)

5. Equation 5:
   \(12x - 3 = 12\)
   \(12x = 12 + 3\)
   \(12x = 15\)
   \(x = \frac{15}{12} = \frac{5}{4}\)

Now let's summarize the solutions:

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

The solutions for Equations 2 and 3 are both \(-7\). Equations 1 and 4 have different solutions than \(-7\) and differ from one another as well. However, Equation 5 has a solution of \(\frac{5}{4}\), which is different from all other solutions.

Therefore, the equation with a solution different from the rest is:

Equation 5: \(12x - 3 = 12\).