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We are asked to solve the equation \( 5ax - 2 = 2a(x + 1) \) for \( x \).

### Step-by-step solution:
1. **Expand the right-hand side:**
   \[
   5ax - 2 = 2a(x + 1) \implies 5ax - 2 = 2ax + 2a
   \]

2. **Move all terms involving \( x \) to one side and constants to the other:**
   \[
   5ax - 2ax = 2a + 2 \implies 3ax = 2a + 2
   \]

3. **Solve for \( x \):**
   \[
   x = \frac{2a + 2}{3a}
   \]

The correct answer is \( x = \frac{2a + 2}{3a} \), which matches the second option in the provided choices.

### Would you like further details or clarifications?

Here are 5 related questions to expand your understanding:
1. How do you handle equations with variables on both sides?
2. Can you explain how to factor expressions like \( 2a + 2 \)?
3. What happens when \( a = 0 \) in this equation?
4. How can we apply this method to quadratic equations?
5. Why is it important to simplify equations before solving?

**Tip:** Always distribute terms and combine like terms on both sides of the equation before isolating the variable.

Which equation shows 5ax - 2 = 2a(x + 1) solved for x?

Learn how to solve the linear equation 5ax - 2 = 2a(x + 1) for x with a detailed step-by-step solution. This algebra problem involves expanding, combining like terms, and isolating the variable. Suitable for students in Grades 9-11.

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