Let's solve the equation \( 5x - 8 = 8 - (-8.5x + 1.5) - 3x \).

### Step 1: Simplify the right side of the equation.
Distribute the negative sign inside the parentheses on the right side:
\[
5x - 8 = 8 + 8.5x - 1.5 - 3x
\]
Now, combine like terms on the right side:
\[
5x - 8 = 6.5x + 6.5
\]

### Step 2: Get all the \(x\) terms on one side and the constant terms on the other side.
Subtract \(6.5x\) from both sides:
\[
5x - 6.5x - 8 = 6.5
\]
Combine like terms:
\[
-1.5x - 8 = 6.5
\]

### Step 3: Isolate the \(x\) term.
Add 8 to both sides to get:
\[
-1.5x = 14.5
\]

### Step 4: Solve for \(x\).
Divide both sides by \(-1.5\):
\[
x = \frac{14.5}{-1.5} = -\frac{29}{3} = -9.\overline{6}
\]

So, the solution is \(x = -9.\overline{6}\), which can also be written as \(-9.\overline{6}\) or approximately \(-9.67\).

Would you like further clarification or have any questions?

Here are some related questions:
1. How do you handle equations with decimals?
2. What is the process for solving equations with multiple terms on both sides?
3. How can you check your solution for accuracy?
4. How would this process change if the equation were quadratic?
5. What are some strategies for solving more complex equations?

**Tip:** When working with decimals, consider multiplying the entire equation by 10 or 100 to eliminate the decimals, making calculations easier.

Learn how to solve the equation 5x - 8 = 8 - (-8.5x + 1.5) - 3x with a step-by-step solution. This problem involves simplifying expressions, combining like terms, and isolating the variable x. Suitable for high school students studying algebra and equations.

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