Question 367675
{{{x^2+8x-20<0}}}
{{{(x+10)(x-2)<0}}}
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Break up the number line into 3 regions using the critical points of the function.
Region 1:({{{-infinity}}},{{{-10}}})
Region 2:({{{-10}}},{{{2}}})
Region 3:({{{2}}},{{{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=-11}}}
{{{(x+10)(x-2)<0}}}
{{{(-11+10)(-11-2)<0}}}
{{{(-1)(-13)<0 }}}
{{{13<0 }}}
False, Region 1 is not part of the solution region.
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Region 2:{{{x=0}}}
{{{(x+10)(x-2)<0}}}
{{{(10)(-2)<0}}}
{{{-20<0 }}}
True, Region 2 is part of the solution region.
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Region 3:{{{x=3}}}
{{{(x+10)(x-2)<0}}}
{{{(3+10)(3-2)<0}}}
{{{(13)(1)<0 }}}
{{{13<0 }}}
False, Region 3 is not part of the solution region.
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Solution Region:({{{-10}}},{{{2}}})
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Graphical verification: Look for regions where the function is below the x-axis ({{{y<0}}})
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{{{drawing(300,300,-12,4,-40,40,grid(1),blue(line(-10,500,-10,-500)),blue(line(2,500,2,-500)),graph(300,300,-12,4,-40,40,(x+10)(x-2)))}}}