3
algebra

If x6=12\frac{x}{6} = 12, what is the value of xx?

A

0.5

B

18

C

2

D

72

Correct Answer: D

Choice Dhoice C is the correct answer. When the variable is in a fraction, we multiply to isolate it.

  1. Start with the equation: x6=12\frac{x}{6} = 12
  2. Multiply both sides by 6: x=12×6x = 12 \times 6
  3. Calculate: x=72x = 72
  4. Verify: 726=12\frac{72}{6} = 12

💡 Strategy: For xa=b\frac{x}{a} = b, always multiply: x=abx = ab.

Choice Dhoice A is incorrect because this results from dividing 12 by 6 instead of multiplying: 126=2\frac{12}{6} = 2. This divides when we should multiply.

Choice Dhoice C is incorrect because this comes from adding: 12+6=1812 + 6 = 18. Addition is not the inverse of division.

Choice Dhoice D is incorrect because this results from dividing in the opposite direction: 612=0.5\frac{6}{12} = 0.5. This is the reciprocal of Choice Dhoice A.