It seems like there might be a slight confusion or typo in the equation you provided. You wrote:

\[
4(x - 1) = 2x + 64(x - 1) = 2x + 6
\]

This looks like it might be two separate equations, or possibly one combined equation. Could you clarify if these are two separate equations, or if it's one equation?

For now, I'll assume these are two separate equations and solve each one:

### 1. First Equation: \(4(x - 1) = 2x + 6\)

1. **Distribute** the 4 on the left side:
   \[
   4x - 4 = 2x + 6
   \]

2. **Subtract \(2x\) from both sides** to get all \(x\) terms on one side:
   \[
   4x - 2x - 4 = 2x - 2x + 6
   \]
   Simplifying, we get:
   \[
   2x - 4 = 6
   \]

3. **Add 4 to both sides** to isolate the \(x\) term:
   \[
   2x = 10
   \]

4. **Divide both sides by 2** to solve for \(x\):
   \[
   x = 5
   \]

### 2. Second Equation: \(64(x - 1) = 2x + 6\)

1. **Distribute** the 64 on the left side:
   \[
   64x - 64 = 2x + 6
   \]

2. **Subtract \(2x\) from both sides**:
   \[
   64x - 2x - 64 = 2x - 2x + 6
   \]
   Simplifying, we get:
   \[
   62x - 64 = 6
   \]

3. **Add 64 to both sides**:
   \[
   62x = 70
   \]

4. **Divide both sides by 62** to solve for \(x\):
   \[
   x = \frac{70}{62} = \frac{35}{31} \approx 1.13
   \]

So, the solutions are:

- For the first equation: \(x = 5\)
- For the second equation: \(x = \frac{35}{31}\)

Please let me know if this matches what you intended, or if you need further clarification.

---

Here are 8 related questions you might find useful:

1. What would happen if you had similar terms on both sides of the equation?
2. How would you solve an equation like \(5(x - 1) = 3x + 7\)?
3. Can you solve an equation where the coefficients are fractions?
4. How would you check if your solutions are correct?
5. What happens if you multiply both sides of an equation by a constant?
6. Can you explain the importance of isolating the variable in solving equations?
7. How would these steps change for an equation with a quadratic term?
8. What if the equation involved a greater degree of complexity, like logarithms?

**Tip:** When solving multiple equations, solving them separately step by step helps prevent mistakes!

Learn how to solve the equations 4(x - 1) = 2x + 6 and 64(x - 1) = 2x + 6 step-by-step. Includes detailed solutions for each equation involving distribution and fraction handling. Suitable for Grades 7-9.

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