step by step solve (x+1)(x-2)>(x+1)(-x+6)

Question

Advanced functions asap

Answer 1

(x+1)(x-2)>(x+1)(-x+6)    take the rhs over to the lhs

(x+1)(x-2) - (x+1)(-x+6) > 0   take out the common factor of (x+1)

(x+1)(x-2 +x-6) > 0

(x+1)(2x-8) > 0     divide by 2

(x+1)(x-4) > 0

For the above inequality to be true, we require (x+1) and (x-4) to both be positive OR (x+1) and (x-4) to both be negative. i.e.

(x+1) > 0 and (x-4) > 0   OR    (x+1) < 0  and   (x-4) < 0

x > -1  and  x > 4          OR        x < -1  and  x < 4

Now the first option, x > -1  and  x > 4, is satisfied by x > 4.

The second option, x < -1  and  x < 4, is satisfied by x < -1.

We thus require x to be constrained by

x < -1 or x > 4

Answer 2

i think 1<x<2 AND 2<x<4