https://file.aiquickdraw.com/mathbot/file/1726854270044ytbpo55z.jpg

The equation in the image is:

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

To solve this equation, we will use cross-multiplication to eliminate the fractions.

Cross-multiplying gives:
\[
x \cdot 2 = (x + 4) \cdot 3
\]

Simplifying both sides:
\[
2x = 3(x + 4)
\]

Distribute the 3 on the right-hand side:
\[
2x = 3x + 12
\]

Now, isolate \(x\) by subtracting \(3x\) from both sides:
\[
2x - 3x = 12
\]

This simplifies to:
\[
-x = 12
\]

Finally, multiply both sides by \(-1\) to solve for \(x\):
\[
x = -12
\]

So, the solution is \(x = -12\).

Would you like further details or have any questions?

Here are five related questions for practice:
1. What would happen if the right side of the equation was \(\frac{x - 4}{2}\)?
2. Can you verify the solution by substituting \(x = -12\) into the original equation?
3. How would the solution change if the equation was \(\frac{x}{3} = \frac{x + 4}{5}\)?
4. What happens if the denominator on the left side was a variable instead of 3?
5. Can you solve \(\frac{2x}{3} = \frac{x + 4}{4}\)?

**Tip**: Cross-multiplying is a powerful tool when dealing with equations that contain fractions. Always check your solution by substituting it back into the original equation!

This problem involves solving a linear equation by using the cross-multiplication method. The detailed solution explains step-by-step how to simplify the equation and find the value of x. Suitable for students in Grades 7-9.

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