A student solved the equation x + 2 (x + 1) = 17 below and showed their work in the table below.

Question

Problem: x + 2 (x + 1) = 17

Line 1: x + 2x + 2 = 17

Line 2: 3x + 2 = 17

Line 3: 3x = 15

Line 4: x = 45

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Identify the property used to arrive at Line 1. Response area

Identify the property used to arrive at Line 2. Response area

What line has a mistake? Response area

What should have been the correct answer for that line? Response area

The option "Line 3" (7 of 11) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.

Answer 1

Let's go through each line and respond to the prompts accordingly.

1. Identify the property used to arrive at Line 1.
   Response area: Distributive Property.
   (The student distributed 2 across the parentheses in \(2(x + 1)\), turning it into \(2x + 2\).)

2. Identify the property used to arrive at Line 2.
   Response area: Combination of Like Terms.
   (The student combined \(x\) and \(2x\) to get \(3x\).)

3. What line has a mistake?
   Response area: Line 4.
   (The student incorrectly solved for \(x\).)

4. What should have been the correct answer for that line?
   Response area: x = 5.
   (From Line 3, \(3x = 15\), dividing both sides by 3 would give \(x = 5\).)