What is the correct order of the missing justifications to fill in the blanks for the given equation 4(x + 5) = 2x + 2, given the following steps: 4x + 20 = 2x + 2, 2x + 20 = 2, 2x = -18, x = -9?

Answer: The correct order of the missing justifications is as follows:

1. Distributive property

2. Subtraction property of equality

3. Subtraction property of equality

4. Division property of equality

Step-by-step explanation:

To determine the correct order of the missing justifications to fill in the blanks for the given equation 4(x + 5) = 2x + 2, let's analyze the steps provided:

Step 1: 4(x + 5) = 2x + 2

This step represents the original equation.

Step 2: 4x + 20 = 2x + 2

This step applies the distributive property by multiplying 4 by each term inside the parentheses, resulting in 4x + 20 on the left side.

Step 3: 2x + 20 = 2

This step simplifies the equation further by subtracting 2x from both sides, which eliminates the variable term on the right side. The equation becomes 2x + 20 = 2.

Step 4: 2x = -18

This step subtracts 20 from both sides of the equation, resulting in 2x = -18.

Step 5: x = -9

Finally, this step isolates the variable x by dividing both sides of the equation by 2, resulting in the solution x = -9.

Please note that the missing justifications may vary depending on the textbook or curriculum being used. However, based on the given steps, this order aligns with the most common justifications used in solving equations.