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Simplifying (4xq) + (12x(1 + -1q)) = (16xq) + (8x(1 + -1q)) (4qx) + ((1 * 12x + -1q * 12x)) = (16xq) + (8x(1 + -1q)) Reorder the terms: (4qx) + ((-12qx + 12x)) = (16xq) + (8x(1 + -1q)) (4qx) + ((-12qx + 12x)) = (16xq) + (8x(1 + -1q)) (4qx) + (-12qx + 12x) = (16xq) + (8x(1 + -1q)) Remove parenthesis around (-12qx + 12x) (4qx) + -12qx + 12x = (16xq) + (8x(1 + -1q)) Combine like terms: (4qx) + -12qx = -8qx -8qx + 12x = (16xq) + (8x(1 + -1q)) -8qx + 12x = (16qx) + ((1 * 8x + -1q * 8x)) Reorder the terms: -8qx + 12x = (16qx) + ((-8qx + 8x)) -8qx + 12x = (16qx) + ((-8qx + 8x)) -8qx + 12x = (16qx) + (-8qx + 8x) Remove parenthesis around (-8qx + 8x) -8qx + 12x = (16qx) + -8qx + 8x Combine like terms: (16qx) + -8qx = 8qx -8qx + 12x = 8qx + 8x Solving -8qx + 12x = 8qx + 8x Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-8qx' to each side of the equation. -8qx + -8qx + 12x = 8qx + -8qx + 8x Combine like terms: -8qx + -8qx = -16qx -16qx + 12x = 8qx + -8qx + 8x Combine like terms: 8qx + -8qx = 0 -16qx + 12x = 0 + 8x -16qx + 12x = 8x Add '-12x' to each side of the equation. -16qx + 12x + -12x = 8x + -12x Combine like terms: 12x + -12x = 0 -16qx + 0 = 8x + -12x -16qx = 8x + -12x Combine like terms: 8x + -12x = -4x -16qx = -4x Divide each side by '-16x'. q = 0.25 Simplifying q = 0.25
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