To identify which property justifies Step 2 of the solution, let’s analyze the steps carefully:
1. Given: [tex]\( XY = 42 \)[/tex]
2. [tex]\( XZ + ZY = XY \)[/tex]
3. [tex]\( 3(n+4) + 3n = 42 \)[/tex]
4. [tex]\( 3n + 12 + 3n = 42 \)[/tex]
5. [tex]\( 6n + 12 = 42 \)[/tex]
6. [tex]\( 6n = 30 \)[/tex]
7. [tex]\( n = 5 \)[/tex]
Now let's focus specifically on Step 3 which is:
[tex]\[ 3(n+4) + 3n = 42 \][/tex]
In this step, the expression [tex]\( 3(n + 4) \)[/tex] has been expanded. The equation [tex]\( 3(n + 4) + 3n = 42 \)[/tex] involves distributing the multiplier 3 over the terms inside the parentheses, which can be seen in the expanded form:
[tex]\[ 3n + 12 \][/tex]
This process of expanding and eliminating parentheses by distributing the multiplier is defined by the Distributive Property, which states that:
[tex]\[ a(b + c) = ab + ac \][/tex]
Therefore, the property that justifies Step 2 of the solution is:
B. Distributive Property
