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 analyze the student's solution step by step:

The original equation is:
\[ x + 2(x + 1) = 17 \]

### Line 1: Expand the equation
The student rewrote it as:
\[ x + 2x + 2 = 17 \]
This step includes distributing the 2 in \( 2(x + 1) \) properly:

The correct expansion should be:
\[ x + 2x + 2 = 17 \]

### Line 2: Combine like terms
The student then combined like terms:
\[ 3x + 2 = 17 \]

### Line 3: Solve for \( x \)
Next, they subtracted 2 from both sides:
\[ 3x = 17 - 2 \]
\[ 3x = 15 \]

### Line 4: Finally, solve for \( x \)
Now, divide by 3:
\[ x = \frac{15}{3} \]
\[ x = 5 \]

### Conclusion
The student's final answer \( x = \frac{16}{3} \) is incorrect. The correct solution to the equation \( x + 2 (x + 1) = 17 \) should yield \( x = 5 \).