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.
A) Collect Like Terms
B) Subtraction Property of Equalities
C) Distributive Property
D) Addition Property of Equalities

Answer 1

To arrive at Line 1 from the original equation \( x + 2(x + 1) = 17 \), the student combined the terms \( 2(x + 1) \) which involves distributing the \( 2 \) to both \( x \) and \( 1 \).

The proper way to describe this operation is:

• The student expanded \( 2(x + 1) \) using the Distributive Property, which gives \( 2 \cdot x + 2 \cdot 1 = 2x + 2 \).

Thus, combining this with \( x \) gives \( x + 2x + 2 \).

Therefore, the correct answer is:

C) Distributive Property.