How do you solve $w^2-2<=0$ using a sign chart?

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Answer 1 · 2017-09-26T12:43:38

Solution: $-sqrt2 <= w <= sqrt2 or [-sqrt2,sqrt2]$

$w^2-2 <=0 or (w+sqrt2)(w-sqrt2) <= 0$ . Critical points

are $w= sqrt2 and w = -sqrt2$ at $w = +- sqrt2 ; w^2-2=0$

Sign chart:

When $w < -sqrt2$ sign of $(w+sqrt2)(w-sqrt2)$ is $(-)*(-) =+ ; >0$

When $-sqrt2 < w < sqrt2$ sign of $(w+sqrt2)(w-sqrt2)$

is $(+)*(-) =- ; < 0$

When $w > sqrt2$ sign of $(w+sqrt2)(w-sqrt2)$ is $(+)*(+) =+ ; >0$

Solution: $-sqrt2 <= w <= sqrt2 or [-sqrt2,sqrt2]$

graph{x^2-2 [-12.66, 12.65, -6.33, 6.33]} [Ans]

How do you solve w^2-2<=0w^2-2<=0 using a sign chart?