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

##### 1 Answer
Mar 25, 2018

The solution set is $x < - 3 \mathmr{and} x > 1$.

#### Explanation:

${x}^{2} + 2 x > 3$

${x}^{2} + 2 x - 3 > 0$

$\left(x + 3\right) \left(x - 1\right) > 0$

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:

$x < - 3 \mathmr{and} x > 1$

That's the solution. Hope this helped!