SOLUTION: Find and Graph the solution set. a. x^3-16x>0 b. x^2-5x<=-6

Question 327127: Find and Graph the solution set.
a. x^3-16x>0
b. x^2-5x<=-6
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

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.
.
.
.
Region 1:

True, this region is part of the solution.
.
.
.
Region 1:

False, this region is not part of the solution.
.
.
.
Region 2:

True, this region is part of the solution.
.
.
.
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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