Question 472471: solve the inequality, graph the solutin set, express the solution set in interval notation
x^2 ≥ -x +20
and
3x+5
____ ≥ 0
6-2x
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! solve the inequality, graph the solutin set, express the solution set in interval notation
x^2 ≥ -x +20
and
3x+5
____ ≥ 0
6-2x
**
x^2 ≥ -x +20
f(x)=x^2+x-20≥0
f(x)=(x-5)(x+4)≥0
zeros: -4 and -5
number line:
<....+....-4....-....5....+.....>
Explanation:
When x≥5, f(x)>0
As you go thru the zeros, the sign of the intervals switch if the zeros are of odd multiplicity like 1,3,5, etc.
solution: (-∞,-4] U [5,∞)
..
f(x)=(3x+5)/(6-2x)≥0
zeros: -5/3 and 1/3
number line:
<....+....-5/3....-....1/3....+.....>
When x≥1/3, f(x)>0
solution: (-∞,-5/3] U [1/3,∞)
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