It looks like there is a mistake in the final step of the student's solution. Let's go through the steps correctly to solve the equation \( x + 2(x + 1) = 17 \):
-
Distribute \( 2 \) in the expression: \[ x + 2(x + 1) = x + 2x + 2 = 17 \]
-
Combine like terms: \[ x + 2x + 2 = 17 \implies 3x + 2 = 17 \]
-
Subtract \( 2 \) from both sides: \[ 3x + 2 - 2 = 17 - 2 \implies 3x = 15 \]
-
Divide both sides by \( 3 \): \[ x = \frac{15}{3} = 5 \]
So, the corrected final answer should be \( x = 5 \), not \( 45 \).