Set 8: Linear Equations (Advanced)

Choice D is correct. Choice C is the correct answer. When the variable is in a fraction, we multiply to isolate it. 1. Start with the equation: $\frac{x}{6} = 12$ 2. Multiply both sides by 6: $x = 12 \times 6$ 3. Calculate: $x = 72$ 4. Verify: $\frac{72}{6} = 12$ ✓ Strategy: For $\frac{x}{a} = b$, always multiply: $x = ab$. Choice A is incorrect because this results from dividing 12 by 6 instead of multiplying: $\frac{12}{6} = 2$. This divides when we should multiply. Choice C is incorrect because this comes from adding: $12+ 6 = 18$. Addition is not the inverse of division. Choice D is incorrect because this results from dividing in the opposite direction: $\frac{6}{12} = 0.5$. This is the reciprocal of Choice A.