Question 330853
{{{ x^2 - 9 > 0}}} 
{{{(x-3)(x+3)>0}}}
Break up the number line into 3 regions.
Region 1:({{{-infinity}}},{{{-3}}})
Region 2:({{{-3}}},{{{3}}})
Region 3:({{{3}}},{{{infinity}}})
Pick a point in each 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: {{{x=-4}}}
{{{(x-3)(x+3)>0}}}
{{{(-4-3)(-4+3)>0}}}
{{{(-7)(-1)>0}}}
{{{7>0}}}
True, this region is part of the solution.
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Region 2: {{{x=0}}}
{{{(x-3)(x+3)>0}}}
{{{(-3)(3)>0}}}
{{{-9>0}}}
False, this region is not part of the solution.
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Region 3: {{{x=4}}}
{{{(x-3)(x+3)>0}}}
{{{(4-3)(4+3)>0}}}
{{{(1)(7)>0}}}
{{{7>0}}}
True, this region is part of the solution.
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({{{-infinity}}},{{{-3}}})U({{{3}}},{{{infinity}}})
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Graphically, look for the regions where the function is greater than zero (above the x-axis).
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{{{drawing(300,300,-6,6,-6,6,blue(line(-3,10,-3,-10)),blue(line(3,10,3,-10)),graph(300,300,-6,6,-6,6,x^2-9))}}}