To solve the equation \( 115.5 - 5.3x = 5.7x + 23.1 \), follow these steps:

### Step 1: Combine like terms
First, move all the terms involving \( x \) to one side of the equation and the constant terms to the other side. Start by adding \( 5.3x \) to both sides of the equation:

\[
115.5 = 5.7x + 5.3x + 23.1
\]

This simplifies to:

\[
115.5 = 11x + 23.1
\]

### Step 2: Isolate the variable
Next, subtract 23.1 from both sides to isolate the term with \( x \):

\[
115.5 - 23.1 = 11x
\]

This simplifies to:

\[
92.4 = 11x
\]

### Step 3: Solve for \( x \)
Finally, divide both sides by 11 to solve for \( x \):

\[
x = \frac{92.4}{11} = 8.4
\]

So, the solution is \( x = 8.4 \).

Would you like more details or have any questions? 

Here are five related questions you might find interesting:

1. How would the solution change if the constant term 23.1 were increased?
2. Can you graphically represent the solution to the equation?
3. What would the equation look like if it were written in slope-intercept form?
4. How can you check that \( x = 8.4 \) is the correct solution?
5. What is the effect on the solution if the coefficient of \( x \) on one side is doubled?

**Tip:** When solving linear equations, always remember to perform the same operation on both sides to keep the equation balanced.

Learn how to solve the equation 115.5 - 5.3x = 5.7x + 23.1 with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations, variable isolation, and combining like terms. Suitable for students in Grades 7-9.

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