Solve the equation justifying each step with the correct reasoning.

Question

2(x + 8) = 2x + 8
Step 1: ____________ Property to get ____________ simplified equation.
Step 2: ____________ Property to get ____________ simplified equation For this equation, there is/are _____________
Properties and Reasons options: Division of Equality, Combine Like Terms, Subtraction of Equality, Multiplication of Equality, Distributive, Addition of Equality
Equation simplified: One Solution, x + 16 = 8, 16 = 8, No Solution, Infinite Solutions, 2x + 16 = 2x + 8, x = -8, 2x + 8 = 8, x + 8 = 8, 2x + 8 = 2x + 8, x = 2
Fill in the blanks

Answer 1

To solve the equation \(2(x + 8) = 2x + 8\), we will justify each step.

Step 1:

Use the Distributive Property to get: \[ 2x + 16 = 2x + 8 \] This is because the Distributive Property allows us to distribute the 2 across the terms inside the parentheses.

Step 2:

Use the Subtraction of Equality Property to get: \[ 16 = 8 \] We subtract \(2x\) from both sides, which simplifies our equation.

For this equation, there is/are No Solution. This is because \(16 = 8\) is a false statement, indicating that there are no values of \(x\) that will satisfy the original equation.

Here’s how the final answer fills in the blanks:

• Step 1: Distributive Property to get 2x + 16 = 2x + 8 simplified equation.
• Step 2: Subtraction of Equality Property to get 16 = 8 simplified equation.
• For this equation, there is/are No Solution.

Answer 2

are you sure this is correct

Answer 3

Let's go through the solution step by step again to verify the steps and reasoning. The original equation is:

\[ 2(x + 8) = 2x + 8 \]

Step 1:

We will use the Distributive Property to expand the left side of the equation.

Step 1: Distributive Property to get: \[ 2x + 16 = 2x + 8 \]

Step 2:

Next, we can apply the Subtraction of Equality property. We will subtract \(2x\) from both sides of the equation to simplify.

Step 2: Subtraction of Equality Property to get: \[ 16 = 8 \]

Analysis of the Result:

The statement \(16 = 8\) is incorrect (a false statement), which means there are no values of \(x\) that would satisfy the original equation.

Thus, for this equation, there is No Solution.

So the filled-in responses would be:

• Step 1: Distributive Property to get 2x + 16 = 2x + 8 simplified equation.
• Step 2: Subtraction of Equality Property to get 16 = 8 simplified equation.
• For this equation, there is/are No Solution.

This is indeed the correct breakdown of the problem and the reasoning applied. Thank you for your patience!