1/3(3x-6)^3+4 < 13.
1/3(3x-6)^2(3x-6)+4 < 13,
1/3(9x^2-36x+36)(3x-6)+4 < 13,
(3x^2-12x+12)(3x-6)+4 < 13 ,
3(x^2-4x+4)(3x-6)+4 < 13,
3(x^2-4x+4)3(x-2)+4 < 13,
9(x^2-4x+4)(x-2)+4 < 13,
9(x^3-2x^2-4x^2+8x+4x-8)+4 < 13,
9(x^3-6x^2+12x-8)+4 < 13,
9(x^3-6x^2+12x-8)-9 < 0,
Divide both sides by 9:
(x^3-6x^2+12x-8)-1 < 0,
Using synthetic division:
(x-2)(x^2-4x+4)-1 < 0,
(x-2)(x-2)(x-2) < 1,
x-2 < 1,
X < 3.
Solve 1/3(3x-6)^3+4<13
1 answer