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Question 201777: 15x + 3(2x - 7) - 9(4 + 5x)
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! I highly recommend changing subtractions to additions. (In fact in my remedial classes I require it.) My reasons:- Addition is easier for most people
- There are very subtle mistakes that can be made with subtractions.
- Addition is Commutative. Subtraction is not. (Commutative means you can change the order as you please without changing the result.)
- Addition is Associative. Subtraction is not. (Associative means you can change the grouping as you please without changing the result.)
To change subtractions to additions, the rule is: "Subtraction is the same as Addition of the opposite." So we just need to be able to figure out what the "opposite" of something is.
Changing the subtractions in 15x + 3(2x - 7) - 9(4 + 5x) gives:
16x + 3(2x + (-7)) + (-9)(4 +5x)
Now let's go through PEMDAS. P for parentheses. We have two sets of parentheses but we cannot add the terms in either one because they are not like terms.
E for exponents. We have no exponents.
MD for multiply and divide. We can multiply using the Distributive Property giving:
16x + 3*(2x) + 3*(-7) + (-9)(4) + (-9)*(5x)
and then
16x + 6x + (-21) + (-36) + (-45x)
AS for Add and Subtract. Reordering (using the Commutative Property) and Regrouping (using the Associative Property), which we could not do if there was any subtractions, gives:
(16x + 6x + (-45x)) + ((-21) + (-36))
Adding we get:
-23x + (-57)
We've reached the end of PEMDAS and the end of your problem.
If you try this problem without changing the subtractions to additions and you do not get -23x + (-57) (or something equal to it: -23x - 57 or -57 + (-23x) or -57 - 23x), then you've just shown yourself why you should start changing the subtractions.
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