To determine which equation has a different solution, we will solve each equation for \( x \).
A. \( -0.35x - 0.52 = 1.93 \)
Adding \( 0.52 \) to both sides: \[ -0.35x = 1.93 + 0.52 = 2.45 \] Dividing by \( -0.35 \): \[ x = \frac{2.45}{-0.35} \approx -7 \]
B. \( -\frac{1}{7}x - \frac{3}{4} = \frac{1}{4} \)
Adding \( \frac{3}{4} \) to both sides: \[ -\frac{1}{7}x = \frac{1}{4} + \frac{3}{4} = 1 \] Multiplying by \( -7 \): \[ x = -7 \]
C. \( \frac{3}{4}x + 5 = -\frac{1}{4} \)
Subtracting \( 5 \) from both sides: \[ \frac{3}{4}x = -\frac{1}{4} - 5 = -\frac{1}{4} - \frac{20}{4} = -\frac{21}{4} \] Multiplying by \( \frac{4}{3} \): \[ x = -\frac{21}{4} \cdot \frac{4}{3} = -7 \]
D. \( \frac{1}{2}x - 3 = \frac{1}{2} \)
Adding \( 3 \) to both sides: \[ \frac{1}{2}x = \frac{1}{2} + 3 = \frac{1}{2} + \frac{6}{2} = \frac{7}{2} \] Multiplying by \( 2 \): \[ x = 7 \]
Now we summarize the solutions of each equation:
- A: \( x \approx -7 \)
- B: \( x = -7 \)
- C: \( x = -7 \)
- D: \( x = 7 \)
The solution that is different from the rest is from equation D, which has \( x = 7 \), while the other three equations all yield \( x = -7 \). Therefore, the correct answer is:
D. 1/2x − 3 = 1/2