Question

which graph represents the solution for x² + x - 12 > 0?

Explanation:

Step1: Factor the quadratic inequality

Factor $x^{2}+x - 12$ to get $(x + 4)(x-3)>0$.

Step2: Find the roots

Set $(x + 4)(x - 3)=0$. The roots are $x=-4$ and $x = 3$.

Step3: Test intervals

Test the intervals $x<-4$, $-43$.
For $x<-4$, let $x=-5$, then $(-5 + 4)(-5-3)=(-1)\times(-8)=8>0$.
For $-4For $x>3$, let $x = 4$, then $(4 + 4)(4-3)=8\times1=8>0$.

The solution of the inequality $x^{2}+x - 12>0$ is $x<-4$ or $x>3$.

Answer:

The graph with open - circles at $x=-4$ and $x = 3$ and arrows pointing to the left of $x=-4$ and to the right of $x = 3$. (The fourth graph in the order presented in the question)