To solve the equation \( 2(x + 4) = 3(2x - 8) \), follow these steps:

1. **Distribute** the constants on both sides:
   \[
   2 \cdot x + 2 \cdot 4 = 3 \cdot 2x - 3 \cdot 8
   \]
   This simplifies to:
   \[
   2x + 8 = 6x - 24
   \]

2. **Move the variable terms** to one side of the equation and the constants to the other:
   \[
   2x - 6x = -24 - 8
   \]
   Simplifying gives:
   \[
   -4x = -32
   \]

3. **Solve for \(x\)** by dividing both sides by \(-4\):
   \[
   x = \frac{-32}{-4}
   \]
   Simplifying gives:
   \[
   x = 8
   \]

So, the solution is \( x = 8 \).

Would you like more details on this solution, or do you have any further questions?

Here are 5 related questions you might find interesting:
1. How do you solve an equation with variables on both sides?
2. What are the steps to check if the solution to an equation is correct?
3. How do you solve inequalities that involve distribution?
4. Can you explain how to handle equations with fractions?
5. What happens if an equation has no solution or infinite solutions?

**Tip:** Always distribute and combine like terms before moving terms to one side of the equation. This simplifies solving and reduces errors.

Learn how to solve the equation 2(x + 4) = 3(2x - 8) step-by-step with a detailed solution. This problem involves algebraic concepts such as distribution and equation solving techniques. Suitable for students in Grades 7-9.

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