A student solved the equation: x+2(x+1)=17

Question

Step 1: x+2x+2=17
Step 2: 3x+2=17
Step 3: 3x=15
Step 4: x=45
(3 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.
Identify the property used to arrive at Step 1: Response area

What step includes a mistake made from the previous step? Response area

What should have been the correct answer for x ? Response area

Answer 1

Let's break down your questions step by step:

1. Identify the property used to arrive at Step 1:
   The student is using the Distributive Property to expand the left side of the equation $x+2(x+1)=17$ into $x+2x+2=17$.

2. What step includes a mistake made from the previous step?
   The mistake is made in Step 4, where the student states $x=45$. This is incorrect based on the calculations leading up to this step.

3. What should have been the correct answer for x?
   After correctly solving $3x=15$, the correct calculation for x should be: $$x=\frac{15}{3}=5$$

So, the answers are:

1. Identify the property used to arrive at Step 1: Distributive Property
2. What step includes a mistake made from the previous step? Step 4
3. What should have been the correct answer for x? 5