Solve the Fraction Equation: Finding X in 1/6x - 1/3 = 1/3

To solve the equation $\frac{1}{6}x - \frac{1}{3} = \frac{1}{3}$, we will take the following steps:

• Step 1: Eliminate fractions by multiplying the entire equation by the least common multiple of the denominators $6$.
• Step 2: Simplify the resulting equation.
• Step 3: Isolate the variable $x$.

Let's proceed with the solution:

Step 1: Multiply the entire equation by $6$ to clear fractions:
$6 \left(\frac{1}{6}x - \frac{1}{3}\right) = 6 \times \frac{1}{3}$

Step 2: Simplify:
$x - 2 = 2$

Step 3: Solve for $x$ by adding $2$ to both sides:
$x = 2 + 2$

Therefore, $x = 4$.