Solve the Fraction Equation: Find X in 1/6(x-4) = 1/4(1/3x+3)

To solve the equation $\frac{1}{6}(x-4) = \frac{1}{4}(\frac{1}{3}x+3)$, follow these steps:

• Step 1: Clear fractions by finding a common multiple.
  The least common multiple of 6 and 4 is 12. Multiply both sides by 12 to eliminate the fractions.
  $12 \times \left( \frac{1}{6} \right)(x-4) = 12 \times \left( \frac{1}{4} \right)\left( \frac{1}{3}x + 3 \right)$.
• Step 2: Simplify both sides.
  On the left side: $2(x-4) = 2x - 8$.
  On the right side: $3\left( \frac{1}{3}x + 3 \right) = x + 9$.
• Step 3: Set the simplified expressions equal.
  $2x - 8 = x + 9$.
• Step 4: Solve the linear equation for $x$.
  Subtract $x$ from both sides: $2x - x = 9 + 8$.
  This simplifies to $x = 17$.

Therefore, the solution to the equation is $x = 17$.