Question 132830
What is the solution of: -x^2+x>=-20? 
Answer choices:
A) x<=-4 or x>=5
B) -4<=x<=5
C) x<=-5 or x>=4
D) -5<=x<=4

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-x^2 + x >= - 20

Bring +20 to the left side.

-x^2 + x + 20 = >= 0

-x^2 + 5x - 4x + 20 >= 0

Set into groups:

x(-x + 5) 4(-x + 5) >= 0

(x + 4) (-x + 5) > = 0

Set each factor to zero and solve for x.

x + 4 >= 0

x >= - 4

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NEXT:

-x + 5 >= 0

-x >= -5

We now divide both sides by -1, which is the coefficient of x.
However, when we divide by a negative number, we MUST reverse the sign of the inequality.

x <= 5

We have this solution for x:

x >= - 4
x <= 5

Final answer: Choice B

Is this clear?