To solve the equation:

\[
\frac{2}{3}x = \frac{4}{9}
\]

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 3 to eliminate the denominator on the left-hand side:

\[
3 \times \frac{2}{3}x = 3 \times \frac{4}{9}
\]

This simplifies to:

\[
2x = \frac{12}{9}
\]

### Step 2: Simplify the right-hand side
Simplify \(\frac{12}{9}\):

\[
2x = \frac{4}{3}
\]

### Step 3: Solve for \(x\)
Now, divide both sides of the equation by 2:

\[
x = \frac{\frac{4}{3}}{2} = \frac{4}{3} \times \frac{1}{2} = \frac{4}{6} = \frac{2}{3}
\]

So the solution is:

\[
x = \frac{2}{3}
\]

Would you like any further details or have any questions?

Here are 5 related questions to expand your understanding:
1. What happens when both sides of an equation are multiplied by the same number?
2. How would you solve \(\frac{5}{4}x = \frac{3}{2}\)?
3. What are common strategies for solving equations with fractions?
4. How would you verify the solution of an equation like this?
5. How does solving equations differ when dealing with improper fractions?

**Tip:** Always try to simplify fractions at every step to make solving easier.

Master the solution to the linear equation 2/3x = 4/9 with our comprehensive guide. This tutorial covers key algebraic concepts such as fractions, equation-solving techniques, and the properties of equality, ideal for students in Grades 6-8.

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