Given (x+2) (x-3) < - 3x + 2

Question

1)Solve for x. 2)Determine the sum of all the integers satisfying the expression x^2 + 2x - 8

Answer 1

(1) x²-x-6<-3x+2,

x²+2x-8<0,

(x+4)(x-2)<0,

Either x+4<0 and x-2>0, implying x<-4 and x>2 (impossible); or:

x+4>0 and x-2<0, implying x>-4 and x<2, so the solution is:

-4<x<2 or x in (-4,2) interval.

(2)

I guess you mean all integers satisfying x²+2x-8<0.

Answer is -3-2-1+1=-5.