How do you solve $1/2x^2>=4-x$ using a sign chart?

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Answer 1 · 2017-05-15T11:30:03

Solution: $x<=-4 and x>=2 or (-oo, -4] uu [2,oo)$

$1/2 x^2 >= 4-x or x^2 >= 8- 2x or x^2 +2x -8 >=0$ or

$x^2 +4x-2x -8 >=0 or x(x+4) -2 (x+4) >= 0 or (x+4)(x-2) >=0$

Critical points are $x= -4 , x=2$

Sign chart:
When $x < -4$ $(x+4) (x-2) is (-)*(-) = (+) , >0$

When $-4 < x < 2 (x+4)(x-2) is (+)*(-)= - <0$

When $x > 2$ $(x+4) (x-2) is (+)*(+) = (+) >0$

Solution $x<=-4 and x>=2 or (-oo, -4] uu [2,oo)$ [Ans]

How do you solve 1/2x^2>=4-x1/2x^2>=4-x using a sign chart?