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The image contains an equation-solving problem that requires filling in the blanks. The equation given is:

\[
\frac{3x}{5} - \frac{x - 6}{3} = 10
\]

Let's solve this step by step.

1. First, find the common denominator and rewrite the equation:
   \[
   \frac{3x}{5} - \frac{x - 6}{3} = 10
   \]

   The common denominator between 5 and 3 is 15. Rewrite both fractions with a denominator of 15:
   \[
   \frac{3x}{5} = \frac{9x}{15}, \quad \frac{x - 6}{3} = \frac{5(x - 6)}{15}
   \]

2. Now the equation is:
   \[
   \frac{9x}{15} - \frac{5(x - 6)}{15} = 10
   \]

   Combine the fractions:
   \[
   \frac{9x - 5(x - 6)}{15} = 10
   \]

3. Simplify the numerator:
   \[
   9x - 5(x - 6) = 9x - 5x + 30 = 4x + 30
   \]

   So the equation becomes:
   \[
   \frac{4x + 30}{15} = 10
   \]

4. Multiply both sides of the equation by 15 to eliminate the denominator:
   \[
   4x + 30 = 150
   \]

5. Solve for \(x\):
   \[
   4x = 150 - 30 = 120
   \]

   \[
   x = \frac{120}{4} = 30
   \]

Thus, the solution to the equation is \(x = 30\).

Would you like me to fill in the blanks in the problem based on this solution?

Here are some related questions:
1. How do you find a common denominator in fraction-based equations?
2. Why is it necessary to eliminate the denominator when solving equations?
3. What are the steps involved in simplifying terms within parentheses?
4. How can you check your solution to ensure it's correct?
5. What should you do if the solution to an equation involves negative numbers?

**Tip:** Always simplify each step before moving to the next to avoid confusion when solving complex equations!

Solve the equation: (3x / 5) - ((x - 6) / 3) = 10

Learn how to solve the linear equation (3x/5) - ((x-6)/3) = 10 using step-by-step methods like finding a common denominator, simplifying, and solving for x. This problem is ideal for students in Grades 7-9 studying algebraic fractions.

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