+501 Find all x that satisfy the inequality (2x+10)(x+3)<(3x+9)(x+8). Express your answer in interval notation.
+130466 (2x + 10) ( x + 3) < (3x + 9) (x + 8) simplify both sides
2x^2 + 10x + 3*2x + 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
Note that when
x > - 3 this is true
-14 < x < -3 it is false
x < -14 it is true
So
( - inf, -14 ) U ( -3, inf) are the intervals that make this true
