Question

graph the solution to the following inequality on the number line.
$x^{2}+4xleq12$
note that you can use the aleks graphing calculator to help get your answer.

Explanation:

Step1: Rearrange the inequality

$x^{2}+4x - 12\leqslant0$

Step2: Factor the quadratic expression

$(x + 6)(x - 2)\leqslant0$

Step3: Find the roots

Set $(x + 6)(x - 2)=0$. Then $x=-6$ or $x = 2$.

Step4: Test intervals

Test the intervals $x<-6$, $-62$.
For $x<-6$, let $x=-7$, then $(-7 + 6)(-7 - 2)=(-1)\times(-9)=9>0$.
For $-6For $x>2$, let $x=3$, then $(3 + 6)(3 - 2)=9\times1=9>0$.

Answer:

The solution is $-6\leqslant x\leqslant2$. On the number - line, you would place a closed circle at $x=-6$ and $x = 2$ and shade the region between them.