Let's solve the equation step by step:

Given equation:
\[
4x - 5x - 9 = 5x - 9
\]

### Step 1: Simplify both sides.
First, combine like terms on the left side:
\[
-x - 9 = 5x - 9
\]

### Step 2: Move all terms involving \( x \) to one side.
Add \( x \) to both sides to eliminate the \( -x \) on the left:
\[
-9 = 6x - 9
\]

### Step 3: Move the constant term to the other side.
Add 9 to both sides to eliminate the \( -9 \) on the right:
\[
0 = 6x
\]

### Step 4: Solve for \( x \).
Divide both sides by 6:
\[
x = 0
\]

So, the solution is:
\[
x = 0
\]

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:
1. How do you solve \( 3x - 2 = 2x + 7 \)?
2. What is the process to solve \( 2(x - 3) = 4x + 1 \)?
3. Can you solve an equation with variables on both sides, like \( 7x + 4 = 5x + 10 \)?
4. How do you handle equations with multiple terms, like \( 3x + 4 - 2x = 6x - 5 + x \)?
5. What if the equation was \( -x - 9 = -5x + 9 \)? How would you solve that?

**Tip:** Always simplify the equation as much as possible before solving for the variable. This makes the problem easier to manage!

Learn how to solve the equation 4x - 5x - 9 = 5x - 9 with a detailed step-by-step solution. This problem involves simplification, variable isolation, and basic algebraic solution techniques. Suitable for high school students.

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