https://file.aiquickdraw.com/mathbot/file/1726525404892kc4b4p82.jpg

The equation extracted from the image seems to be:

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

Now, let's solve this step-by-step.

### Step 1: Eliminate the fractions
To clear the denominators, multiply the entire equation by the least common denominator (LCD), which is 45 (LCM of 5 and 9).

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

This simplifies to:

\[
9(x - 4) = 45 \times 9 - 5(2x - 41)
\]

### Step 2: Expand both sides
Now expand both sides:

\[
9x - 36 = 405 - 10x + 205
\]

Simplify:

\[
9x - 36 = 610 - 10x
\]

### Step 3: Collect like terms
Move all the \(x\) terms to one side and the constants to the other side:

\[
9x + 10x = 610 + 36
\]

\[
19x = 646
\]

### Step 4: Solve for \(x\)
Divide both sides by 19:

\[
x = \frac{646}{19} = 34
\]

Thus, the solution is:

\[
x = 34
\]

Would you like further clarification or details on any step?

### Related questions:
1. What if the equation had different denominators?
2. How would you check if the solution is correct?
3. How do you solve similar equations with more than two fractions?
4. What if the equation had an inequality instead of an equality?
5. How would you solve this equation graphically?

### Tip: Always check for extraneous solutions when solving rational equations by plugging your solution back into the original equation.

Solve the equation: (x - 4)/5 = 9 - (2x - 41)/9

Learn how to solve the equation (x - 4)/5 = 9 - (2x - 41)/9 step by step. This problem includes algebraic concepts like cross-multiplication, combining like terms, and solving linear equations with fractions. Suitable for Grades 8-10.

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