To solve the equation \( 9(x - 4) = 2(x + 3) \), follow these steps:

1. Distribute the 9 and the 2:
   \[
   9x - 36 = 2x + 6
   \]

2. Move all terms involving \( x \) to one side of the equation and constants to the other side. Subtract \( 2x \) from both sides:
   \[
   9x - 2x - 36 = 6
   \]
   Simplify:
   \[
   7x - 36 = 6
   \]

3. Add 36 to both sides to isolate the term with \( x \):
   \[
   7x - 36 + 36 = 6 + 36
   \]
   Simplify:
   \[
   7x = 42
   \]

4. Divide both sides by 7 to solve for \( x \):
   \[
   x = \frac{42}{7}
   \]
   Simplify:
   \[
   x = 6
   \]

So, the solution to the equation is \( x = 6 \).

Would you like more details or have any questions?

Here are some related questions:

1. What if the equation was \( 9(x - 4) = 2(x + 3) + 10 \)?
2. How do you solve \( 5(x - 2) = 3(x + 4) \)?
3. What steps would you take to solve \( 8(x + 5) = 4(x - 2) \)?
4. How can you verify the solution \( x = 6 \) is correct for the original equation?
5. What if the equation was \( 9(x - 4) = 2(x + 3) + x \)?
6. How do you solve \( 12(x - 3) = 4(2x + 1) \)?
7. What is the solution to \( 7(x + 2) = 5(x + 6) \)?
8. How do you solve \( 3(x - 1) = 6(x - 2) \)?

**Tip:** When solving linear equations, always simplify both sides of the equation first and then isolate the variable on one side.

Learn how to solve the linear equation 9(x - 4) = 2(x + 3) with detailed steps. This problem involves the distributive property and solving linear equations. Suitable for students in Grades 7-9.

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