SOLUTION: 1/5 (-5a +20b) - 1/2(2b-6a) Every source I find has the second a value being positive after distributing the half. They say it as b + 3a, and I always get it as b - 3a. How does

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: 1/5 (-5a +20b) - 1/2(2b-6a) Every source I find has the second a value being positive after distributing the half. They say it as b + 3a, and I always get it as b - 3a. How does      Log On


   



Question 1097237: 1/5 (-5a +20b) - 1/2(2b-6a)
Every source I find has the second a value being positive after distributing the half. They say it as b + 3a, and I always get it as b - 3a. How does 1/2 (2b - 6a) become b + 3a? How does the - get changed to a plus? I get -4a + 3b whenever I finish the problem, but every source I find says the answer is 2a + 3b. The sources are this website, mathpapa.com, and my in-class answer sheet by my teacher. Thank you.

Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
1/5 (-5a +20b) - 1/2(2b-6a)
distribute the 1/5 over the -5a to get -a and over 20b to get 4b
The first term is -a+4b
distribute the (-1/2) over 2b to get -b and over -6a to get +3a (two minuses make a plus)
The second term is -b+3a
Adding them would be 3b+2a
The second term has a negative b term, because the (-1/2), and one takes the minus sign with the 1/2
The a is already negative, so the -1/2 will make it positive.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

1/5 (-5a +20b) - 1/2(2b-6a)
Every source I find has the second a value being positive after distributing the half. They say it as b + 3a, and I always get it as b - 3a. How does 1/2 (2b - 6a) become b + 3a? How does the - get changed to a plus? I get -4a + 3b whenever I finish the problem, but every source I find says the answer is 2a + 3b. The sources are this website, mathpapa.com, and my in-class answer sheet by my teacher. Thank you.
It is INDEED 2a + 3b.
It's not
%281%2F5%29%28-+5a+%2B+20b%29+-+%281%2F2%29%282b+-+6a%29
------ Distributing terms

highlight_green%28matrix%281%2C3%2C+-+a+%2B+4b+-+b+%2B+3a%2C+%22=%22%2C+2a+%2B+3b%29%29