Let's solve the equation \( 5x + 9 = 17x - 4x + 81 \).

### Step 1: Simplify the equation.
First, combine the like terms on the right side of the equation:

\[
17x - 4x = 13x
\]

So the equation becomes:

\[
5x + 9 = 13x + 81
\]

### Step 2: Get all \( x \) terms on one side.
Subtract \( 5x \) from both sides to move the \( x \) terms to one side:

\[
9 = 13x - 5x + 81
\]

This simplifies to:

\[
9 = 8x + 81
\]

### Step 3: Isolate the \( x \) term.
Subtract 81 from both sides to isolate the \( x \) term:

\[
9 - 81 = 8x
\]

\[
-72 = 8x
\]

### Step 4: Solve for \( x \).
Divide both sides by 8:

\[
x = \frac{-72}{8} = -9
\]

So, the solution is \( x = -9 \).

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. What if the equation was \( 5x + 9 = 20x - 4x + 81 \)?
2. How would the solution change if \( 5x + 9 = 17x + 4x + 81 \)?
3. Can you solve \( 7x + 3 = 2x + 15 \) using similar steps?
4. How do you solve the equation if it is in the form \( ax + b = cx + d \)?
5. What are the steps to solve a system of linear equations like \( 2x + 3y = 7 \) and \( x - y = 1 \)?

**Tip:** Always simplify both sides of an equation as much as possible before trying to solve for the variable.

Learn how to solve the equation 5x + 9 = 17x - 4x + 81 step-by-step. This problem involves algebraic equations and simplification techniques. Suitable for students in Grades 7-9.

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