Question

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

negative 0.35 x minus 0.52 equals 1.93

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

Start Fraction 1 over 2 End Fraction x minus 3 equals Start Fraction 1 over 2 End Fraction

Start Fraction 3 over 4 End Fraction x plus 5 equals negative Start Fraction 1 over 4 End Fraction

Answer 1

To find the equation with a solution different from the rest, we need to solve each of the equations.

1. **Equation 1**: \(-0.35x - 0.52 = 1.93\)

\(-0.35x = 1.93 + 0.52\)

\(-0.35x = 2.45\)

\(x = \frac{2.45}{-0.35} \approx -7\)

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**: \(\frac{1}{2}x - 3 = \frac{1}{2}\)

\(\frac{1}{2}x = \frac{1}{2} + 3\)

\(\frac{1}{2}x = \frac{1}{2} + \frac{6}{2} = \frac{7}{2}\)

\(x = 7\)

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

\(\frac{3}{4}x = -\frac{1}{4} - 5\)

\(\frac{3}{4}x = -\frac{1}{4} - \frac{20}{4} = -\frac{21}{4}\)

\(x = -7\)

Now, let's summarize the solutions:

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

The third equation has a solution \(x = 7\), which is different from the others, which all have the solution \(x = -7\).

Therefore, the equation that has a solution different from the rest is:

**Start Fraction 1 over 2 End Fraction x minus 3 equals Start Fraction 1 over 2 End Fraction.**