Solving Rational Inequalities: (3x+1)/(2x-4) > 0

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SUMMARY

The discussion focuses on solving the rational inequality (3x + 1) / (2x - 4) > 0. The solution involves determining the intervals where both the numerator and denominator are either positive or negative. The critical points identified are x < 1/3 and x > 2, leading to the conclusion that the solution set is x > 2. The importance of analyzing both cases—positive and negative—is emphasized for a complete understanding of the inequality.

PREREQUISITES
  • Understanding of rational inequalities
  • Knowledge of critical points and interval testing
  • Familiarity with the properties of inequalities
  • Basic algebra skills for manipulating expressions
NEXT STEPS
  • Study the method of interval testing for rational inequalities
  • Learn about critical points and their significance in inequality solutions
  • Explore the concept of sign charts for visualizing solutions
  • Review advanced topics in algebra, such as polynomial inequalities
USEFUL FOR

Students studying algebra, educators teaching rational inequalities, and anyone preparing for standardized tests that include inequality problems.

wiiyogi
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Homework Statement



3x+1
2x-4 > 0


The Attempt at a Solution


My answer came to be
(x< 1/3) U (x>2)
 
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Hi wiiyogi

key is you need both denomintor & numerator either positive or negative

so x>2 looks right (need x>-1/3 numerator, x>2 denominator so x>2)

however your negativr case needs another look
 

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