To solve the equation:

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

we first eliminate the fractions by finding a common denominator or by multiplying both sides by the least common multiple (LCM) of the denominators. Here, the LCM of 3 and 2 is 6. So, we multiply both sides by 6:

\[
6 \cdot \frac{x + 2}{3} = 6 \cdot \frac{2x - 4}{2}.
\]

Simplify both sides:

\[
2(x + 2) = 3(2x - 4).
\]

Now distribute on both sides:

\[
2x + 4 = 6x - 12.
\]

Next, isolate the variable \(x\) by moving all terms involving \(x\) to one side and the constants to the other side:

\[
2x - 6x = -12 - 4.
\]

Simplify:

\[
-4x = -16.
\]

Now, solve for \(x\) by dividing both sides by \(-4\):

\[
x = \frac{-16}{-4} = 4.
\]

### Final Answer

The solution to the equation is:

\[
\boxed{x = 4}.
\]

Would you like more details or have any other questions?

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Here are 5 related questions to explore:

1. How do you solve equations with multiple fractions on both sides?
2. How can you check if your solution to an equation is correct?
3. What are some common mistakes to avoid when solving linear equations?
4. How do you solve linear equations with variables on both sides?
5. What is the graphical interpretation of the solution to a linear equation?

**Tip:** When solving equations with fractions, clear the fractions by multiplying by the least common multiple (LCM) to simplify your calculations.

Learn how to solve the equation (x + 2)/3 = (2x - 4)/2 with a detailed step-by-step solution. This problem covers equations with fractions and algebraic manipulations. Suitable for students in Grades 9-12.

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