Question

Solve for x. Answer with Interval Notation.

x^2+5x<24

Answer 1

Answer:

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

Step-by-step explanation:

Answer 2

Answer:

-8 < x < 3

Step-by-step 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