Let's solve the equation \( 4(8x - 1) = 2(2x - 2) \) step by step.

### Step 1: Distribute the constants
Distribute the 4 on the left side and the 2 on the right side:
\[
4 \times 8x - 4 \times 1 = 2 \times 2x - 2 \times 2
\]
This simplifies to:
\[
32x - 4 = 4x - 4
\]

### Step 2: Move all the terms involving \(x\) to one side
Subtract \(4x\) from both sides:
\[
32x - 4x - 4 = -4
\]
This simplifies to:
\[
28x - 4 = -4
\]

### Step 3: Move the constant term to the other side
Add 4 to both sides:
\[
28x = 0
\]

### Step 4: Solve for \(x\)
Divide both sides by 28:
\[
x = 0
\]

### Final Answer:
\[
x = 0
\]

Would you like any more details or have any questions?

Here are 5 related questions you might find interesting:
1. What happens if you add or subtract the same value from both sides of an equation?
2. How do you solve linear equations with variables on both sides?
3. What are the steps to check if a solution is correct for an equation?
4. How do you handle equations involving fractions?
5. Can you solve equations that have quadratic terms?

**Tip:** Always double-check your solution by substituting the value back into the original equation!

Learn how to solve the equation 4(8x − 1) = 2(2x − 2) step-by-step with detailed explanations and a final answer of x = 0. This problem involves algebraic equations and the distributive property, suitable for students in Grades 7-9.

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