Question

How do you solve and write the following in interval notation: `x^2-1x-30>0`?

Answer 1

Solution : `x <-5 or x >6`. In interval notation: `(-oo , -5) uu (6,oo)`.

Explanation:

`x^2-x-30 >0 or x^2-6x+5x-30 >0 or x(x-6) +5(x-6) >0 or (x+5)(x-6)>0`
Critical points are `x = -5 , x =6`

When `x < -5; (x+5)(x-6) is (-)*(-) = (+) or >0`

When `-5< x < 6; (x+5)(x-6) is (+)*(-) = (-) or <0`

When `x > 6; (x+5)(x-6) is (+)*(+) = (+) or >0`

Solution : `x <-5 or x >6`. In interval notation: `(-oo , -5) uu (6,oo)`. The graph also confirms the findings. graph{x^2-x-30 [-80, 80, -40, 40]}[Ans]