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)
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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