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

Question

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

GPT-4o mini · Answer

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 $2 x + 2$ . Thus, Line 1 correctly shows the equation as $x + 2 x + 2 = 17$ .