SOLUTION: Could you please help me with this? I have a huge final this week. I believe the answer is they are all real numbers. Am I correct? Thanks for all your help!! (x+8)(x-13)(x+3)>0

Algebra ->  Inequalities -> SOLUTION: Could you please help me with this? I have a huge final this week. I believe the answer is they are all real numbers. Am I correct? Thanks for all your help!! (x+8)(x-13)(x+3)>0      Log On


   

Question 467415: Could you please help me with this? I have a huge final this week. I believe the answer is they are all real numbers. Am I correct? Thanks for all your help!!
(x+8)(x-13)(x+3)>0
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, find the zeros of y=%28x%2B8%29%28x-13%29%28x%2B3%29.


(x+8)(x-13)(x+3)=0

x+8=0 or x-13=0 or x+3=0

x=-8, x=13, or x=-3


In ascending order, the zeros are: -8,-3,13


Now in the interval , (x+8)(x-13)(x+3) is negative. Simply plug in any negative number less than -8 to see this (eg: plug in x=-10 to get (-10+8)(-10-13)(-10+3)=-322)


In the interval , (x+8)(x-13)(x+3) is positive. Simply plug in any number in the interval to see this (eg: plug in x=-5 to get (-5+8)(-5-13)(-5+3)=108)



In the interval , (x+8)(x-13)(x+3) is negative. Simply plug in any number in the interval to see this (eg: plug in x=0 to get (0+8)(0-13)(0+3)=-312)


Finally, in the interval , (x+8)(x-13)(x+3) is positive. Simply plug in any number greater than 13 to see this (eg: plug in x=50 to get (50+8)(50-13)(50+3)=113738)




So the following intervals make (x+8)(x-13)(x+3) positive: and



So combine them with a union symbol to get the final answer:


Here's a graph to visually confirm this


+graph%28+500%2C+500%2C+-10%2C+18%2C+-1200%2C+1000%2C+%28x%2B8%29%28x-13%29%28x%2B3%29%29+

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Could you please help me with this? I have a huge final this week. I believe the answer is they are all real numbers. Am I correct? Thanks for all your help!!
(x+8)(x-13)(x+3)>0
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1st: Find the values x cannot take: x = -8, x = 13, x = -3
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2nd: Draw a number line and plot those value thur forming
4 intervals of the number line.
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3rd: Test a value from each of the intervals in the inequality to
see where the solutions are:
Test x = -10: -*-*- >0; false
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Test x = -5: +*-*- > 0; true so solutions in (-8,-3)
---
Test x = 0: +*-*+ > 0 ; false
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Test x = 20: +*+*+ > 0; true so solutions in (13,oo)
==========================================================
Solustions: (-8,-3) or (13,oo)
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Cheers,
stan H.