Question

Solve for x. Answer with Interval Notation.

x^2+5x<24

Answer 1

Look for a pair of factors of

24

whose difference is

5 . 24 = 8 × 3 and 5 = 8 − 3 So x 2 + 5 x − 24 = x 2 + ( 8 − 3 ) x − ( 8 × 3 ) = ( x + 8 ) ( x − 3 )

So the solutions of x 2 + 5 x − 24 = 0 are x = − 8 and x = 3

Explanation:

Answer 2

-8 < x < 3

Explanation:

We are given the following quadratic inequality and we are to solve it for x, giving answer with interval notation:

`x^2 + 5x < 24`

`x^2 + 5x - 24 < 0`

`x^2 + 8x - 3x - 24 < 0`

`x (x + 8) - 3 (x+8) < 0`

`(x + 8) (x - 3) < 0`

`(x+8)<0, (x-3)<0`

`x>-8, x<3`

-8 < x < 3