Question

solve for x and graph the solution.

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

plot the endpoints. select an endpoint to change it from a segment, ray, or line to delete it.

Explanation:

Step1: Factor the quadratic inequality

Factor $x^{2}+3x + 2$ to get $(x + 1)(x+2)>0$.

Step2: Find the roots

Set $(x + 1)(x + 2)=0$. Then $x+1 = 0$ gives $x=-1$ and $x + 2=0$ gives $x=-2$. These are the critical - points.

Step3: Test the intervals

We have three intervals to test: $x<-2$, $-2-1$.
For $x<-2$, let $x=-3$. Then $(-3 + 1)(-3 + 2)=(-2)\times(-1)=2>0$, so the inequality is satisfied on the interval $x<-2$.
For $-2For $x>-1$, let $x=0$. Then $(0 + 1)(0 + 2)=2>0$, so the inequality is satisfied on the interval $x>-1$.

Answer:

The solution of the inequality $x^{2}+3x + 2>0$ is $x<-2$ or $x>-1$. On the number - line, we have an open circle at $x=-2$ and an open circle at $x=-1$. We draw a ray to the left of $x=-2$ and a ray to the right of $x=-1$.