https://file.aiquickdraw.com/mathbot/file/172584366346220hze69r.jpg

The equation from the image is:

\[
\frac{x}{5} = \frac{x+2}{9}
\]

To solve for \(x\), let's follow these steps:

1. **Cross-multiply** to eliminate the denominators:
   \[
   9x = 5(x + 2)
   \]

2. **Expand** the equation:
   \[
   9x = 5x + 10
   \]

3. **Isolate the variable** by moving terms involving \(x\) to one side:
   \[
   9x - 5x = 10
   \]
   \[
   4x = 10
   \]

4. **Solve for \(x\)**:
   \[
   x = \frac{10}{4} = 2.5
   \]

So, the solution is \(x = 2.5\).

Would you like further clarification, or do you have any questions about this process?

Here are 5 related questions to deepen your understanding:
1. How would you solve the equation if there were different constants in the denominators?
2. Can this process of cross-multiplication be applied to any rational equation?
3. What happens if one side of the equation is already simplified to a constant?
4. Can you think of real-world problems that use ratios similar to this?
5. How would the equation change if the fraction included a square term in \(x\)?

**Tip:** Always check your solution by substituting the value of \(x\) back into the original equation.

Solve for x in the equation: x/5 = (x+2)/9

Learn how to solve the rational equation x/5 = (x+2)/9 by applying cross-multiplication. This problem involves key algebraic concepts and is suitable for students in Grades 7-9. Follow the detailed steps to isolate x and find the solution.

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