https://file.aiquickdraw.com/mathbot/file/17240308141115cmzqzyx.jpg

The image is quite small, so I might need your help confirming the details. However, I can attempt to interpret the problem based on the visible equation.

If the equation displayed is:
\[
\frac{1}{2} + \frac{1}{6} + \frac{1}{3} \times \left(\frac{1}{9} - \frac{1}{x} \right)
\]

And you need to find the value of \(x\), here's how to proceed:

1. Start with the expression inside the parentheses:
   \[
   \frac{1}{9} - \frac{1}{x}
   \]

2. Multiply this by \(\frac{1}{3}\):
   \[
   \frac{1}{3} \times \left(\frac{1}{9} - \frac{1}{x}\right) = \frac{1}{27} - \frac{1}{3x}
   \]

3. Add all terms together:
   \[
   \frac{1}{2} + \frac{1}{6} + \left(\frac{1}{27} - \frac{1}{3x}\right)
   \]

To solve for \(x\), you would typically set this expression equal to a given value, but since the image isn't clear about what the equation equals, I'll assume it equals zero for demonstration:

\[
\frac{1}{2} + \frac{1}{6} + \frac{1}{27} - \frac{1}{3x} = 0
\]

4. Combine like terms:
   Find a common denominator and add the fractions:
   \[
   \frac{27}{54} + \frac{9}{54} + \frac{2}{54} - \frac{1}{3x} = 0
   \]
   Simplifying:
   \[
   \frac{38}{54} = \frac{19}{27} = \frac{1}{3x}
   \]

5. Solve for \(x\):
   Cross-multiply to get:
   \[
   19x = 81 \quad \Rightarrow \quad x = \frac{81}{19} = 4.26 \text{ (approximately)}
   \]

However, the exact value of \(x\) would depend on the correct interpretation of the problem, especially the equation it's set equal to.

Please confirm if there's a specific value the equation should equal, or if this interpretation is correct. If not, I can correct it accordingly.

Would you like any further clarification? Here are five questions to expand your understanding:

1. How do you solve an equation that includes fractions?
2. Why do we need to find a common denominator when adding fractions?
3. What is the process for cross-multiplication when solving for \(x\)?
4. How can simplifying fractions help in solving equations?
5. What does it mean to solve an equation for \(x\)?

**Tip:** Always check your equation carefully to ensure each step follows logically from the previous one. This avoids mistakes and leads to a correct solution.

Learn how to find the value of x in an equation involving fractions and cross-multiplication with a detailed step-by-step solution. This problem covers key algebraic concepts, including equations with fractions and cross-multiplication technique. Suitable for high school students.

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