Solve the Fraction Equation: Find X in 2/3x - 4/6 = 1/3

Let's solve the equation $\frac{2}{3}x - \frac{4}{6} = \frac{1}{3}$.

Step 1: Simplify the fractions.

• The term $\frac{4}{6}$ is equivalent to $\frac{2}{3}$ after simplification.

Now, the equation can be rewritten as:

$\frac{2}{3}x - \frac{2}{3} = \frac{1}{3}$

Step 2: Add $\frac{2}{3}$ to both sides to isolate the term with $x$.

$\frac{2}{3}x = \frac{1}{3} + \frac{2}{3}$

Simplify the right side:

$\frac{2}{3}x = \frac{3}{3}$

$\frac{3}{3} = 1$

So the equation becomes:

$\frac{2}{3}x = 1$

Step 3: Solve for $x$ by multiplying both sides by the reciprocal of $\frac{2}{3}$.

Multiply both sides by $\frac{3}{2}$:

$x = 1 \times \frac{3}{2}$

Thus, the solution is:

$x = \frac{3}{2}$

The solution to the problem is $x = \frac{3}{2}$.