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

Question

Responses

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

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

−1/7x−3/4=1/4
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

3/4x+5=−1/4

Answer 1

To determine which equation has a solution different from the rest, we can solve each equation for \( x \).

1. Equation 1:
   \(-0.35x - 0.52 = 1.93\)
   \(-0.35x = 1.93 + 0.52\)
   \(-0.35x = 2.45\)
   \(x = \frac{2.45}{-0.35}\)
   \(x \approx -7\)

2. Equation 2:
   \(\frac{1}{2}x - 3 = \frac{1}{2}\)
   \(\frac{1}{2}x = \frac{1}{2} + 3\)
   \(\frac{1}{2}x = \frac{1}{2} + \frac{6}{2}\)
   \(\frac{1}{2}x = \frac{7}{2}\)
   \(x = 7\)

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

4. Equation 4:
   \(\frac{3}{4}x + 5 = -\frac{1}{4}\)
   \(\frac{3}{4}x = -\frac{1}{4} - 5\)
   \(\frac{3}{4}x = -\frac{1}{4} - \frac{20}{4}\)
   \(\frac{3}{4}x = -\frac{21}{4}\)
   \(x = -7\)

Now, we summarize the solutions we found:

1. \( x \approx -7 \)
2. \( x = 7 \)
3. \( x = -7 \)
4. \( x = -7 \)

The equation with a solution different from the rest is Equation 2, which has the solution \( x = 7 \), while the others have the solution \( x \approx -7 \).