Question

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


Line 1: x+2x+1=17


Line 2: 3x+1=17


Line 3: 3x=16


Line 4: x=16/3

Answer 1

Let's review the student's steps solving the equation \( x + 2(x + 1) = 17 \).

1. **Start with the original equation:**
\[
x + 2(x + 1) = 17
\]

2. **Distribute the \(2\) in Line 1:**
\[
x + 2x + 2 = 17
\]

3. **Combine like terms in Line 2:**
\[
3x + 2 = 17
\]

4. **Subtract \(2\) from both sides to isolate the term with \(x\) in Line 3:**
\[
3x = 15
\]

5. **Divide both sides by \(3\) to solve for \(x\) in Line 4:**
\[
x = 5
\]

So the final solution to the equation \( x + 2(x + 1) = 17 \) is \( x = 5 \).

**Correction to the student's work:**
- The student incorrectly simplified the expression \( 2(x + 1) \). It should be \( 2x + 2 \), leading to the equation \( 3x + 2 = 17 \) instead of \( 3x + 1 = 17 \).
- As a result, their final answer of \( x = \frac{16}{3} \) is incorrect. The correct answer is \( x = 5 \).