How do you solve x^2>=36 using a sign chart?

Aug 3, 2016

$x \in \left(\infty , - 6\right] \cup \left[6 , \infty\right)$

Explanation:

${x}^{2} \ge 36$

Let us take the equation first .

${x}^{2} = 36$

$x = \pm 6$

Divide the number line into 3 parts , use this x values
Check which interval satisfies the inequality ${x}^{2} \ge 36$
In the interval $\left(- \infty , - 6\right)$ choose a point say x=-7
x^2=49 so x^2>=36#

In the interval $\left(- 6 , 6\right) , x = 0 , {x}^{2} = 0 , {x}^{2} < 36$
in the interval $\left(6 , \infty\right) , x = 7 ,$x^2=49 , ${x}^{2} \ge 36$

First and 3rd interval satisfies the inequality . we have >=

$x \in \left(\infty , - 6\right] \cup \left[6 , \infty\right)$