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Question 342402: The instructions say "Use properties and definitions of operations to show that the statement is true. Justify each step." The question is 6(a+3)=2a
Answer by Jk22(389)   (Show Source):
You can put this solution on YOUR website! Well, we suppose 6(a+3)=2a were true, without knowing the nature of a
Properties used :
-Distributivity of product towards sum, lhs : 6a+6*3=2a
-Existence of inverse of 6a : -6a :
6a+6a+6*3=-6a+2a
-Right Distributivity : -6a+2a=(-6+2)*a=-4a
-Left regularity : -4*-18/4=-4a => -18/4=a=-9/2
Verif : 6(-9/2+3)=6(-9+6)/2=3*-3=-9
2*a=2*-9/2=-9, true.
Hence, this statement is true if a is in the set containing the rational numbers.
However, this statement were wrong if a were specified to remain in the set of integer number.
(a=-4 : -6=-8, wrong, a=-5 : -12=-10 wrong too)
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