Question

Solve the inequality below. Write your final answer in interval notation. To earn full credit please include all steps/work/calculations and thinking. You may want to do the work by hand on paper and share an image of that work. If you choose to type then to indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters.x^2-x > 12

Answer 1

We must solve the inequality:

`x^2-x>12`

1) We rewrite the inequality:

`x^2-x-12>0`

2) We factorise the polynomial at the left:

`(x+3)(x-4)>0`

3) We have two possibilities.

`\begin{gathered} (x-4)>0\rightarrow x>4, \\ or \\ (x+3)<0\rightarrow x<-3 \end{gathered}`

Solutions

`\begin{gathered} x<-3\text{ or }x>4, \\ (-\infty,-3)\cup(4,\infty) \end{gathered}`