Determine the real solutions of inequality (x-4)(x+8) < (x-8)(x+4).

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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 <...

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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

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