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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
Answer by nycsharkman(136)   (Show Source):
You can put this solution on YOUR website! 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?
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