To solve the equation $\frac{1}{3} + \frac{4}{5} = \frac{x}{9}$, let's follow these steps:

Step 1: Find a common denominator for $\frac{1}{3} + \frac{4}{5}$

The least common denominator (LCD) of 3 and 5 is 15.

Now, rewrite both fractions: $\frac{1}{3} = \frac{5}{15}, \quad \frac{4}{5} = \frac{12}{15}$

Step 2: Add the two fractions

$\frac{5}{15} + \frac{12}{15} = \frac{17}{15}$

Step 3: Set up the equation

Now, the equation becomes: $\frac{17}{15} = \frac{x}{9}$

Step 4: Solve for $x$

To solve for $x$, cross-multiply: $17 \times 9 = 15 \times x$ $153 = 15x$

Step 5: Divide both sides by 15

$x = \frac{153}{15} = 10.2$

Thus, the solution is: $x = 10.2$

Would you like more details or have any questions?

---

Here are 5 related questions to explore further:

1. How do you simplify fractions with different denominators?
2. What are some other ways to solve equations with fractions?
3. How do you find the least common denominator in general?
4. Can this method be used for solving more complex equations?
5. How do you handle equations where fractions appear on both sides?

Tip: Always simplify fractions at the end of solving equations to avoid unnecessary complications.