+96 Find all x that satisfy the inequality (2x+10)(x+3)<(3x+9)(x+8). Express your answer in interval notation.
+129852 (2x+10)(x+3)<(3x+9)(x+8)
2x^2 + 10x + 6x +30 < 3x^2 + 9x + 24x + 72
2x^2 + 16x + 30 < 3x^2 + 33x + 72 rearrange as
x^2 + 17x + 42 > 0 factor as
(x + 14) ( x + 3) > 0
Notice that if x < -14 this is true
Notice that if x is on the interval (-14, -3) this is false
And if x > -3 this is true
So....the solution is
(-inf, -14) U ( -3 , inf )
