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 \( x = 5 \).