The given statement is "If [tex]\( x = y \)[/tex], then [tex]\( x + 4 = y + 4 \)[/tex]".
To determine which property of equality this statement represents, let's analyze it step-by-step:
1. Starting Point: The initial equation is [tex]\( x = y \)[/tex].
2. Adding a Constant to Both Sides: According to the statement, if we add the same number, which is 4, to both sides of the equation [tex]\( x = y \)[/tex], the equality is maintained.
When we perform the addition:
[tex]\[ x + 4 = y + 4 \][/tex]
This operation represents the addition property of equality, which states that adding the same quantity to both sides of an equation does not change the equality.
Therefore, the correct answer is:
D) addition
