Question

How do you solve `X^2 +2X > 3`?

Answer 1

The solution set is `x<-3 or x>1`.

Explanation:

`x^2+2x>3`

`x^2+2x-3>0`

`(x+3)(x-1)>0`

Since we're trying to find when the function is greater than `0`, and the parabola opens upwards, that means the inequality is true whenever `x` is NOT between the zeroes.

This makes more sense if you look at the graph:

graph{x^2+2x-3 [-11, 9, -5, 5]}

Since the zeroes are `-3` and `1`, the inequality is less than `-3` or greater `1`, or:

`x<-3 or x>1`

That's the solution. Hope this helped!