She regrouped the numbers instead of multiplying like 8b(2b-r) -4r(2b-r).
Call the number : x
(1/3)x + 5 = x-6
=> (1/3)x + 5 - (x-6) = 0
=> (1/3)x + 5 - x + 6 = 0
Group (1/3)x with -x, 5 with 6
=> [(1/3)x - x] + (5+6) = 0
=> (-2/3)x + 11 = 0
=> (-2/3)x = -11
=> x = -11 : (-2/3) = 33/2.
Recheck : 1/3 x 33/2 + 5 = 33/6 + 5 = 63/6 = 21/2
33/2 - 21/2 = 12/2 = 6 (21/2 is 6 less than 33/2, satisfied.)
The weight is dropped from 4 feet above the surface. Add -12 to represent the distance the weight falls before it hits the bottom. 4+(-12)=8. The water is 8 feet deep.
(Prezi online)
It belongs in rational numbers because if you converted it into a decimal, it would only be .25. If it was a number like pi, then it would be an irrational number because there is almost no end to it.