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 analyze the student's steps:

1. The first equation was: \( x + 2(x + 1) = 17 \)

2. In Step 1, the student distributed the \(2\):

   • Correctly: \( x + 2x + 2 = 17 \)
   • Property used: Distributive Property

3. In Step 4, the student made a mistake when solving for \(x\):

   • The correct calculation from Step 3 should be: \( x = \frac{15}{3} = 5 \)
   • The answer given (x = 45) is incorrect.

Now, we can fill in the response areas:

1. Identify the property used to arrive at Step 1:

   • Response area: Distributive Property

2. What step includes a mistake made from the previous step?

   • Response area: Step 4

3. What should have been the correct answer for x?

   • Response area: 5