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.
(1 point)
Responses
Collect Like Terms
Collect Like Terms
Subtraction Property of Equalities
Subtraction Property of Equalities
Distributive Property
Distributive Property
Addition Property of Equalities
1 answer
The property used to arrive at Line 1, where the student rewrote the equation from \( x + 2(x + 1) = 17 \) to \( x + 2x + 2 = 17 \), is the Distributive Property. This property allows you to distribute a multiplication over addition or subtraction. Here, \( 2 \) was distributed to both \( x \) and \( 1 \) in the expression \( 2(x + 1) \).
So the correct response is:
Distributive Property
