I set up 1 / 3(12 + x) as a fraction and set it equal to - 8(6 - x).
Get rid of the parentheses by distributing the integers on the outside. You get 1 / 36 + 3x = - 48 + 8x.
To get rid of the fraction, you multiply both sides by the (36 + 3x) polynomial to get 1 = (- 48 + 8x)(36 + 3x).
Now we do the FOIL method to get 1 = 24x^2 + 288x - 144x - 1728. Combine like terms to get 24x^2 + 144x - 1728 = 1.
Simply again by dividing each term the GCF of 24 to get 24(x^2 + 6x - 72) = 1.
Factor the inside of the parentheses to get 24(x + 12)(x - 6) = 1. Now divide both sides by 24 to isolate the x variables to get (x + 12)(x - 6) = 1/24.
Set each polynomial equal to 1/24 to get you possible answers for what x can be.
x + 12 = 1/24. Subtract 12 from both sides; you get x = - 12 + 1/24 to get x = - 11 23/24.
x - 6 = 1/24. Add 6 to both sides; you get x = 6 + 1/24 to get x = 6 1/24
In a proper volleyball ready position, the knees are bent, the hands are out in front of the player at waist level and just outside the knees, and the player's weight is balanced forward.
