Find all x that satisfy the inequality \((2x+10)(x+3)<(3x+9)(x+8)\). Express your answer in interval notation.
+128474 (2x + 10) (x + 3) < (3x + 9) (x + 8) simplify
2x^2 +10x + 6x + 30 < 3x^2 + 9x + 24x + 72
2x^2 + 16x + 30 < 3x^2 + 33x + 72
0 < x^2 + 17x + 42
x^2 + 17x + 42 > 0 factor
(x + 14) ( x + 3) > 0
Set each factor to 0 and solve for x and we have that x = -14 and x = -3......
So....we have the following posible solution intervals ... (-infinity, -14) or (-14, -3) or (-3, infinity)
When the interval on x is from
(- infinity, -14) ⇒ (x + 14) (x + 3) is > 0
( -14, -3) ⇒ (x + 14) ( x + 3) is < 0
(-3, infinity) ⇒ (x + 14) (x + 3) is > 0
So.....the solution intervals lie on ( -infinity , -14) U ( -3 , infinity )
