How to write the solution in interval notation?

Question

0>(2x-9)(x+4)

thanks

Answer 1

For the product to be less than zero (negative) one yet not both of the factors must be less than zero (negative).

1.

2x - 9 < 0 ⇒ 2x < 9 ⇒ x < 9/2

x + 4 > 0 ⇒ x > -4

(-4, 9/2)

2.

2x - 9 > 0 ⇒ 2x > 9 ⇒ x > 9/2

x + 4 < 0 ⇒ x < -4

no intersection

 

(-4, 9/2)