Which equation must be true? A x−y=y−x B m÷p=p÷m C (d−e)−f=d−(e−f) D (r+s)+t=r+(s+t)

Question
Linear equations and graphs
asked 2021-01-24
Which equation must be true?
A x−y=y−x
B m÷p=p÷m
C (d−e)−f=d−(e−f)
D (r+s)+t=r+(s+t)

Answers (1)

2021-01-25
Subtraction is not commutative. For example, 3−2  =  2−3 since 3−2=1 and 2−3=−1. The equation x−y=y−x must then be false.
Division is also not commutative. For example, 4÷2  =  2÷4 since 4÷2=2 and 2÷4=1. The second equation m÷p=p÷mm÷p=p÷m must then be false.
Subtraction is also not associative. Distributing the negative on the right side of the equation (d−e)−f=d−(e−f) gives (d−e)−f=d−e+f. The two sides are then not equal since the left side has −f and the right side has ff. The third equation is then false.
Addition is associative. The Associative Property of Addition states that (a+b)+c=a+(b+c). Therefore (r+s)+t=r+(s+t). The correct answer is then choice D.
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