To solve the equation \( \frac{2x + 3}{3} = \frac{4x + 2}{3} \) for \( x \), follow these steps:

### Step 1: Eliminate the fractions
Since the denominators on both sides of the equation are the same, you can multiply both sides by 3 to eliminate the fractions:

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

This simplifies to:

\[
2x + 3 = 4x + 2
\]

### Step 2: Rearrange the equation to isolate \( x \)
Subtract \( 2x \) from both sides:

\[
3 = 2x + 2
\]

Then subtract 2 from both sides:

\[
1 = 2x
\]

### Step 3: Solve for \( x \)
Divide both sides by 2:

\[
x = \frac{1}{2}
\]

So, \( x = \frac{1}{2} \).

Would you like more details on any step, or do you have any questions?

### Related Questions:
1. What happens if the fractions have different denominators?
2. How would you solve a similar equation if there were variables in the denominator?
3. Can you solve an equation like this using substitution?
4. What if the equation had a higher degree, like \( x^2 \) or \( x^3 \)?
5. How does cross-multiplication work in equations like this?

### Tip:
Always check your solution by substituting it back into the original equation to ensure both sides are equal.

Learn how to solve the equation 2x + 3/3 = 4x + 2/3 step-by-step. This problem involves equations with fractions, suitable for students in Grades 7-9.

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