Question 353487
{{{(3x-1)/(x-7)<=4}}}
{{{(3x-1)/(x-7)-4<=0}}}
{{{(3x-1)/(x-7)-(4(x-7))/(x-7)<=0}}}
{{{(3x-1-4(x-7))/(x-7)<=0}}}
{{{(3x-1-4x+28)/(x-7)<=0}}}
{{{(27-x)/(x-7)<=0}}}
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Break up the number line into 3 regions using the critical points from the equation.
Region 1:({{{-infinity}}},{{{7}}})
Region 2:({{{7}}},{{{27}}})
Region 3:({{{27}}},{{{infinity}}})
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For each region pick a test point (not an endpoint).
Test the inequality.
If the inequality is satisfied, the region is part of the solution region.
Region 1:{{{x=0}}}
{{{(27-x)/(x-7)<=0}}}
{{{(27)/(-7)<=0}}}
{{{-27/7<=0}}}
True, this region is part of the solution.
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Region 2:{{{x=10}}}
{{{(27-10)/(10-7)<=0}}}
{{{17/3<=0}}}
False, this region is not part of the solution.
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Region 1:{{{x=30}}}
{{{(27-30)/(30-7)<=0}}}
{{{-3/23<=0}}}
True, this region is part of the solution.
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Solution region: ({{{-infinity}}},{{{7}}}) U ({{{27}}},{{{infinity}}})