We are given the equation:

\[
x - \frac{4}{5} = 9 - 2x - \frac{41}{9}
\]

### Steps to solve:

1. **Eliminate fractions by finding the least common denominator (LCD):**

   The LCD of 5 and 9 is 45. Multiply every term of the equation by 45 to eliminate the fractions:

   \[
   45 \left( x - \frac{4}{5} \right) = 45 \left( 9 - 2x - \frac{41}{9} \right)
   \]

   Expanding both sides:

   \[
   45x - \left( \frac{4 \times 45}{5} \right) = 45(9) - 45(2x) - \left( \frac{41 \times 45}{9} \right)
   \]

   Simplifying:

   \[
   45x - 36 = 405 - 90x - 205
   \]

   This simplifies further to:

   \[
   45x - 36 = 200 - 90x
   \]

2. **Move all \(x\)-terms to one side and constants to the other side:**

   Add \(90x\) to both sides:

   \[
   45x + 90x - 36 = 200
   \]

   Combine like terms:

   \[
   135x - 36 = 200
   \]

3. **Solve for \(x\):**

   Add 36 to both sides:

   \[
   135x = 236
   \]

   Divide both sides by 135:

   \[
   x = \frac{236}{135}
   \]

   Simplifying the fraction, we get:

   \[
   x = \frac{236}{135} \quad \text{(This fraction cannot be simplified further)}
   \]

Thus, the solution is:

\[
x = \frac{236}{135}
\]

---

Would you like a more detailed explanation or have any questions?

### 5 Related Questions:
1. How do you solve linear equations with fractions?
2. How can you simplify complex fractions in equations?
3. What are the steps to find the least common denominator (LCD)?
4. How do you isolate the variable in an equation?
5. How do you check if your solution to an equation is correct?

### Tip: 
Always simplify fractions as much as possible when solving equations to avoid unnecessary complexity!

Learn how to solve the linear equation x - 4/5 = 9 - 2x - 41/9 by eliminating fractions and isolating the variable. This problem covers key algebraic concepts such as working with fractions and solving linear equations. Suitable for students in Grades 8-10.

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