6/(x-8)=2/(x+6)
times both sides by (x-8)(x+6)
6(x+6)=2(x-8)
distribute
6x+36=2x-16
minus 2x both sides
4x+36=-16
miinus 36 both sides
4x=-52
divide both sides by 4
x=-13
The first answer, using a number line, is a good answer.
I have two other ways:
Way #1:
5 stones is more than 3 stones.
5 gallons is greater than 3 gallons.
5 pounds is greater than 3 pounds.
5 puppies is greater than 3 puppies.
5 hamburgers is greater than 2 hamburgers.
5 schoolbuses is greater than 3 schoolbuses.
We look around us, and we see that 5 of anything
is always greater than 3 of the same thing.
There's no reason that should change if the 'things' are eighths.
Way #2:
-- Get 2 friends to help you.
-- Take one good-size veggie pizza or coconut cream pie.
-- Carefully cut it up in eight (8) equal pieces.
Now each piece is 1/8 of the pie or the pizza.
-- Give 5 pieces (5/8) to the first friend.
Give 3 pieces (3/8) to the other friend.
-- Ask them to get together and agree on who has more.
