Question

Solve the equation justifying each step with the correct reasoning.
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

are you sure this is correct

Answer 2

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 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!