How do you solve $x^{2} \geq 36$ $x^2>=36$ using a sign chart?

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How do you solve $x^{2} \geq 36$ $x^2>=36$ using a sign chart?

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Answer 1 · 2016-08-03T11:43:38

$x \in (\infty, - 6] \cup [6, \infty)$ $x in(oo,-6]uu[6,oo)$

Explanation:

$x^{2} \geq 36$ $x^2>=36$

Let us take the equation first .

$x^{2} = 36$ $x^2=36$

$x = \pm 6$ $x=+-6$

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

In the interval $(- 6, 6), x = 0, x^{2} = 0, x^{2} < 36$ $(-6,6) , x=0,x^2=0 , x^2<36$
in the interval $(6, \infty), x = 7,$ $(6,oo) , x=7 ,$ x^2=49 , $x^{2} \geq 36$ $x^2>=36$
enter image source here

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

$x \in (\infty, - 6] \cup [6, \infty)$ $x in(oo,-6]uu[6,oo)$

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How do you solve $x^{2} \geq 36$ $x^2>=36$ using a sign chart?

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