Determine the real solutions of inequality (x-4)(x+8) < (x-8)(x+4).
We have to find all the real solution of (x-4)(x+8) < (x-8)(x+4).
(x-4)(x+8) < (x-8)(x+4)
=> x^2 - 4x + 8x - 32 < x^2 - 8x + 4x - 32
=> -4x + 8x < -8x + 4x
=> 4x < -4x
=> 8x < 0
=> x < 0
The values are all real numbers x satisfying the relation x < 0
First, we'll remove the brackets both sides. We'll apply FOIL method to multiply the terms inside brackets:
x^2 + 8x - 4x - 32 < x^2 + 4x - 8x - 32
We'll move all terms to the left side:
x^2 + 8x - 4x - 32 - x^2 - 4x + 8x + 32 < 0
We'll combine like terms and we'll eliminate like terms:
8x < 0
We'll divide by 8:
x < 0
The solution for the inequality is: x < 0 <=>(-infinite ; 0).