SOLUTION: When four is divided by the sum of a number and seven, the result is the same as half the difference of twice the number and one. find all such numbers. So far i was able to get

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Question 809108: When four is divided by the sum of a number and seven, the result is the same as half the difference of twice the number and one. find all such numbers.
So far i was able to get 4 over x+7 is equal to 2x-1 for my equation but im not sure what to do next or if that is correct.
Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website!
let x be the number
4 / (x+7) = (2x - 1) / 2
cross multiply the two fractions
8 = (x+7) * (2x-1)
8 = 2x^2 +13x -7
subtract 8 from both sides of =
2x^2 +13x -15 = 0
factor the equation
(2x+15)*(x-1) = 0
1) x-1 = 0
x = 1
2) 2x+15 = 0
x = -15/2 = -7.5
check the answers
for x = 1
4/(1+7) = (2*1 -1) / 2
4/8 = 1/2
1/2 = 1/2
for x = -7.5
4/(-7.5+7) = (2*-7.5 -1) / 2
4/-.5 = -16 / 2
-8 = -8
our answers check out, x=1 and x=-7.5