To solve the equation \(6x - 8 = 8 - 6x\), let's follow these steps:

### Step 1: Move all terms involving \(x\) to one side of the equation.
We can add \(6x\) to both sides to eliminate the \(-6x\) on the right-hand side.

\[
6x - 8 + 6x = 8 - 6x + 6x
\]

This simplifies to:

\[
12x - 8 = 8
\]

### Step 2: Move constant terms to the other side.
Now, add \(8\) to both sides to eliminate the \(-8\) on the left-hand side.

\[
12x - 8 + 8 = 8 + 8
\]

Simplifying:

\[
12x = 16
\]

### Step 3: Solve for \(x\).
To isolate \(x\), divide both sides of the equation by \(12\):

\[
x = \frac{16}{12}
\]

Simplifying the fraction:

\[
x = \frac{4}{3}
\]

So, the solution is \(x = \frac{4}{3}\).

Would you like more details or have any questions?

Here are five related questions:
1. How would you solve \(7x - 5 = 5 - 7x\)?
2. Can you solve \(3x + 2 = 10 - x\)?
3. What if the equation was \(8x - 10 = 2x + 4\)?
4. How can you check if the solution \(x = \frac{4}{3}\) is correct?
5. Can you solve \(5x - 3 = 2x + 9\)?

**Tip:** When solving equations, always aim to move variables to one side and constants to the other to simplify the equation.

Learn how to solve the linear equation 6x - 8 = 8 - 6x with a step-by-step guide. This problem demonstrates key algebraic principles such as moving variables and constants, applying equality properties, and simplifying linear expressions. Ideal for students in Grades 6-8.

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