A student solved the equation x + 2(x+1) = 17 below and showed their work in the table below.

Question

Problem: x + 2 (x + 1) = 17
Line 1: x + 2x + 2 = 17
Line 2: 3x + 2 = 17
Line 3: 3x = 15
Line 4: x = 5
Identify the property used to arrive at Line 1.

Answer 1

The property used to arrive at Line 1 from the original equation \( x + 2(x + 1) = 17 \) is the Distributive Property.

In Line 1, the student expanded the expression \( 2(x + 1) \) by distributing the \( 2 \) to both \( x \) and \( 1 \), resulting in \( 2x + 2 \). Thus, Line 1 correctly shows the equation as \( x + 2x + 2 = 17 \).