Fractional Equation Challenge: Solve for X in 1/3(1/3x + 1/6) = 1/18

To solve this problem, we'll follow these steps:

• Step 1: Distribute and expand the equation.
• Step 2: Eliminate the fractions by multiplying through by the least common denominator.
• Step 3: Solve for $x$.

Now, let's work through each step:

Step 1: Distribute $\frac{1}{3}$ across the terms in the parentheses:
$\frac{1}{3} \left(\frac{1}{3}x + \frac{1}{6}\right)$ becomes $\frac{1}{3} \cdot \frac{1}{3}x + \frac{1}{3} \cdot \frac{1}{6}$, resulting in $\frac{1}{9}x + \frac{1}{18}$.

Step 2: The equation is now $\frac{1}{9}x + \frac{1}{18} = \frac{1}{18}$.
To eliminate the fractions, we identify the least common denominator, which is 18.

Multiply everything by 18 to clear the fractions:

$18 \cdot \frac{1}{9}x + 18 \cdot \frac{1}{18} = 18 \cdot \frac{1}{18}$

Which simplifies to:

$2x + 1 = 1$

Step 3: Solve the resulting linear equation:

Subtract 1 from both sides to isolate the term with $x$:
$2x = 0$

Divide both sides by 2 to solve for $x$:
$x = 0$

Therefore, the solution to the problem is $x = 0$.