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Greta says that the expression (2xa)+5 is the same as 2x(a+5). Is she correct?  

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brookeg22 | Student | eNotes Newbie

Posted April 24, 2013 at 9:46 PM via web

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Greta says that the expression (2xa)+5 is the same as 2x(a+5). Is she correct?

 

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steveschoen | College Teacher | (Level 3) Assistant Educator

Posted April 24, 2013 at 10:29 PM (Answer #1)

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Hi, Brooke,

Since "a" is what's called "a variable", it can represent any number you want.  "You have the power".  So, just literally picking anything, let's say a=3.  So, we would have:

(2x3)+5     and     2x(3+5)

Now, we always do what's in parenthesis first.  So, for the left expression, we do 2x3 first.  2x3 = 6.  Then, adding 5, 6+5 = 11.  So, we have:

(2x3)+5 = 11     and     2x(3+5)

We just haven't done the right one yet.  Now, we do that one.  Always parenthesis first.  So, 3+5 = 8.  Then, we multiply that by the 2 at the beginning.  2x(8) = 16.  So, we have:

(2x3)+5 = 11     and     2x(3+5)=16

So, Brooke, since 11 and 16 are different and not the same, then (2xa)+5 and 2x(a+5) can't be the same.

I hope this assist, Brooke.  Good luck.

Steve

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