Doug C. answered • 12/22/22
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Raminder K.
asked • 12/22/22Solve the inequality:
|(x-3)/(2x-1)|>(3x+1)/(x-1)
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2 Answers By Expert Tutors
Raymond B. answered • 12/22/22
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(-3-sqr89)/10 <x<1/2 or 1/2<x<1
or in interval notation
((-3-sqr89)/10, 1/2) U (1/2, 1)= about (-1.24, .5)U (.5,1)
according to one website calculator
checking the end behavior
as x grows very large or very small, the right hand side is greater than the absolute left side
so
the solution set will be in the middle,
cross multiply the fractions to find potential interval endpoints
x^2-4x +3 = 6x^2 -x -1
5x^2 +3x -4 =0
x=-3/10 +/-(1/10)sqr89 = about -1.24, 0.64
are potential endpoints of intervals solving the inequality, also 1 and 1/2 which make the two fractions' denominators =0
Mark M.
Your point is well taken. Thank you.
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12/24/22
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Mark M.
An absolute value is in an inequality. Therefore it must be solved twice. Once for the argument being positive, once for the argument being negative. This may cause 2x - 1 and x - 1 being negative. Multiplication by either would reverse the inequality.12/22/22