SOLUTION: 15x + 3(2x - 7)

SOLUTION: 15x + 3(2x - 7) - 9(4 + 5x)

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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