SOLUTION: Hello ! Can you please help me with this? I just don't get it... Iwould really appreciate if you could show how to solve it step by step. Many thanks (x-3)^2>=33-4x

Algebra ->  Inequalities -> SOLUTION: Hello ! Can you please help me with this? I just don't get it... Iwould really appreciate if you could show how to solve it step by step. Many thanks (x-3)^2>=33-4x      Log On


   

Question 359105: Hello !
Can you please help me with this? I just don't get it... Iwould really appreciate if you could show how to solve it step by step. Many thanks
(x-3)^2>=33-4x
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-3%29%5E2%3E=33-4x
x%5E2-6x%2B9%3E=33-4x
x%5E2-2x-24%3E=0
%28x-6%29%28x%2B4%29%3E=0
Break up the number line into 3 regions using the critical points of the function.
Region 1:(-infinity,-4)
Region 2:(-4,6)
Region 3:(6,infinity)
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For each region, choose a point in the region (not an endpoint).
Test the inequality.
If the inequality is satisfied, the region is part of the solution region.
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Region 1:x=-5
%28x-6%29%28x%2B4%29%3E=0
%28-5-6%29%28-5%2B4%29%3E=0
%28-11%29%28-1%29%3E0+
11%3E0+
True, Region 1 is part of the solution region.
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Region 2:x=0
%28x-6%29%28x%2B4%29%3E=0
%28-6%29%284%29%3E0+
-24%3E0+
False, Region 2 is not part of the solution region.
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Region 3:x=7
%28x-6%29%28x%2B4%29%3E=0
%287-6%29%287%2B4%29%3E=0
%281%29%2811%29%3E0+
11%3E0+
True, Region 3 is part of the solution region.
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Solution Region: (-infinity,-4] U [6,infinity)
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Graphical verification: Look for regions where the function is above the x-axis (y%3E=0)
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