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Solving Rational Inequalities: A Step-by-Step Guide with Examples, Study notes of Algebra

University of the Philippines Open University Algebra

more careful in finding your solutions. To solve a rational inequality: 1. find the zeroes (from the numerator). 2. find the undefined points (from the ...

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SolvingRationalInequalities

ToBracketorNottoBracket...

SolvingRationalInequalities

Solvingrationalinequalitiesisverysimilartosolvingpolynomial

inequalities.

Thismeansthatwearetryingtofigureoutwhenthefunctionitself

hasavaluegreaterthanorlessthan0.

Butbecauserationalexpressionshavedenominators(andtherefore

mayhaveplaceswherethey'renotdefined),youhavetobealittle

morecarefulinfindingyoursolutions.

Tosolvearationalinequality:

1.findthe

zeroes

(fromthenumerator)

2.findthe

undefinedpoints

(fromthedenominator).

3.usethesezeroesandundefinedpointstodivide

the

numberline

intointervals.

4.

testeachinterval

tofindthesignoftherational

functiononeachinterval.

5.writethefinalsolutionoftheinequalityusing



intervalnotation

.

**Theundefinedpointswillalwayshaveopen

intervals,whiletheintervalsofthezerosdependon

theinequalitysign.**

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To Bracket or Not to Bracket ...