Question
A student solved the equation x + 2 (x + 1) = 17 below and showed their work in the table below.
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.
Answers
GPT-4o mini
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 \(x = 5\).)
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 \(x = 5\).)