Let's analyze the problem presented in the image. The equation given is:

$x + \frac{1}{2}(6x - 4) = 8$

There is a table showing the steps taken to solve the equation, but the justifications are missing. The possible answers refer to various properties such as the distributive property, combining like terms, addition and subtraction properties of equality, and the division property of equality.

Step-by-Step Explanation:

1. Step 1: $x + 3x - 2 = 8$ Here, the distributive property is used. The $\frac{1}{2}(6x - 4)$ is expanded to $3x - 2$.

2. Step 2: $4x - 2 = 8$ Combining like terms: $x + 3x = 4x$.

3. Step 3: $4x = 10$ Addition property of equality is used to add 2 to both sides.

4. Step 4: $x = 2.5$ Division property of equality is used to divide both sides by 4.

Correct Answer:

The correct answer should have these justifications:

1. Distributive Property
2. Combine Like Terms
3. Addition Property of Equality
4. Division Property of Equality

Thus, the correct answer is Option 1.

Would you like further details or explanations on this solution? Here are some related questions you could explore:

1. What is the distributive property and when is it used?
2. How does combining like terms simplify an equation?
3. What are the different properties of equality?
4. How do you solve multi-step linear equations?
5. Why is the division property of equality important in algebra?

Tip: Always check for opportunities to combine like terms early in an equation to simplify your work.