Question

olve the equation justifying each step with the correct reasoning.

2(x+8)=2x+8
(5 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Step 1: ______________Property to get
Step 2: _______________simplified equation

For this equation, there is/are Response area

Properties and Reasons
Equation simplified

Answer 1

Let's solve the equation step by step, providing justifications for each action. The equation to solve is:

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

**Step 1:** Distribute the left side using the Distributive Property.

\[ 2(x+8) = 2 \cdot x + 2 \cdot 8 \rightarrow 2x + 16 \]

This gives us:

\[ 2x + 16 = 2x + 8 \]

**Step 2:** Simplify the equation to isolate the terms on one side. Subtract \( 2x \) from both sides.

\[ 2x + 16 - 2x = 2x + 8 - 2x \rightarrow 16 = 8 \]

Now we have a contradiction (16 = 8), indicating that there is no solution.

**Summary:**

- Step 1: **Distributive Property** to get \( 2x + 16 = 2x + 8 \)
- Step 2: **Simplified equation** to \( 16 = 8 \)

For this equation, there is/are: **no solution**.