Question 327286: Hello. I was hoping someone could please help me with a question that I do not know how to solve.
My question has two parts and is as follows:
Find and graph the solution set:
A. x^3 - 16x > 0
B. x^2 - 5x <= -6
I don't know how to solve these questions because they are raised to different powers, so I don't know how to solve for x.
Also, could you please explain to me how I'd go about graphing these inequalities?
Thank you so much.
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! Solved earlier today
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Break up the number line into 4 regions:
Region 1 : ( , )
Region 2 : (, )
Region 3 : (, )
Region 4 : (, )
Choose a point in the region (not an endpoint).
Test the inequality.
If the inequality is satisfied, the region is part of the solution.
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Region 1:
False, this region is not part of the solution.
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Region 2:
True, this region is part of the solution.
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Region 3:
False, this region is not part of the solution.
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Region 4:
True, this region is part of the solution.
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The solution region is (,) U (,).
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Verified graphically
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Similarly,
Break up the number line into 3 regions:
Region 1 : (, )
Region 2 : (, )
Region 3 : (,)
Choose a point in the region (not an endpoint).
Test the inequality.
If the inequality is satisfied, the region is part of the solution.
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Region 1:
True, this region is part of the solution.
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Region 1:
False, this region is not part of the solution.
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Region 2:
True, this region is part of the solution.
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Region 3:
False, this region is not part of the solution.
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The solution region is [,].
Since the inequality includes the "=" the brackets denote that 2 and 3 are included as part of the solution.
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