Let's solve each equation for \( x \):
A. \( \frac{x}{4} = -1 \)
To isolate \( x \), multiply both sides by 4: \[ x = -1 \times 4 = -4 \]
B. \( \frac{x}{-2} = 2 \)
To isolate \( x \), multiply both sides by -2: \[ x = 2 \times -2 = -4 \]
C. \( -12x = 48 \)
To isolate \( x \), divide both sides by -12: \[ x = \frac{48}{-12} = -4 \]
D. \( 16x = 64 \)
To isolate \( x \), divide both sides by 16: \[ x = \frac{64}{16} = 4 \]
Now, let's summarize the solutions:
- A: \( x = -4 \)
- B: \( x = -4 \)
- C: \( x = -4 \)
- D: \( x = 4 \)
The equation that has a different solution than the rest is D. \( 16x = 64 \), since it yields \( x = 4 \), while all other equations yield \( x = -4 \).