Let's solve the equation:

\[
8(x - 2) = 8(x + 4)
\]

### Step 1: Distribute the 8 on both sides.

\[
8x - 16 = 8x + 32
\]

### Step 2: Subtract \(8x\) from both sides to eliminate the variable on one side.

\[
-16 = 32
\]

This is a contradiction, meaning the equation is **inconsistent**. There is no solution for \(x\) that would satisfy this equation. The equation has **no solution**.

### Conclusion: 
The solution to this equation is that there is no solution, or the equation is inconsistent.

Would you like more details or have any questions?

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Here are 5 related questions:

1. How do you solve equations with variables on both sides?
2. What does it mean when an equation has no solution?
3. Can you explain the difference between an equation with no solution and an identity?
4. How do you solve linear equations involving fractions?
5. What happens if you divide both sides of an equation by a variable?

**Tip:** Always check your solution by substituting it back into the original equation.

Learn how to solve the linear equation 8(x-2) = 8(x+4). This step-by-step guide demonstrates the use of the distributive property and highlights the concept of inconsistent equations, resulting in no solution. Suitable for students in Grades 8-10.

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