4. Solve the equation justifying each step with the correct reasoning.

Question

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: Response area Property to get Response area simplified equation

Step 2: Response area Property to get Response area simplified equation

For this equation, there is/are Response area

Answer 1

To solve the equation \(2(x + 8) = 2x + 8\), let’s go through the steps justifying each one with the correct reasoning.

Step 1

Response area: Distributive Property
Response area simplified equation: \(2x + 16 = 2x + 8\)

Justification: We apply the Distributive Property, which states that \(a(b + c) = ab + ac\). Here, we distribute \(2\) across \(x + 8\).

---

Step 2

Response area: Subtraction Property of Equality
Response area simplified equation: \(16 = 8\)

Justification: We subtract \(2x\) from both sides of the equation. The Subtraction Property of Equality states that if two expressions are equal, subtracting the same amount from both sides will keep the equality true.

---

For this equation, there are no solutions.

Justification: The simplified equation \(16 = 8\) is false, indicating that there is no value of \(x\) that satisfies the original equation.