Question 183229: Solve: (3-x)(2+x)(4+x)>0 How do I figure out the answer and write it in interval notation?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! (3-x)(2+x)(4+x)>0
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1st determine values that "x" CANNOT have.
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X cannot be 3, -2, -4
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Draw a number line and mark -4, -2, and 3 on the line
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The line now has 4 defined intervals. Test a point from each
of the intervals in the INEQUALITYl to see where solutions are.
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The INEQULITY: (3-x)(2+x)(4+x)>0
I'm only check the factor signs as we only what to know if the product
is positive
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Test -5 ; -*-*- > 0 ;false
Test -3 : -*-*+ > 0 ; true so solutions in (-4,-2)
Test 2 : +*+*+ > 0 ; true, so solutions in (-2,3)
Test 4 ; -*+*+ > 0 ; false
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Solution : (-4,-2) U (-2,3)
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Cheers,
Stan H.
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