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1.6 Inequalities # 9-53 oddA closed interval, denoted by ],[ ba, consists of all real numbers x for which bxa .______________________An open interval, denoted by ),( ba, consists of all real numbers x for which bxa .______________________The half-open, or half-closed, intervals are ],( ba, consisting of all real numbers x for which bxa , and ),[ ba, consisting of all real numbers x for which bxa .______________________________________________In each of these definitions, a is called the left endpoint and b is called the right endpoint.),[ a_______________________),( a_______________________],( a_______________________),( a_______________________),( _______________________Example Write each inequality using interval notation.a.31 xb.04  xc.5xd.1xExampleWrite each interval as an inequality involving x.a.)4,1[b.),2( c.]3,2[d.]3,( Working with inequalities is just like working with equalities except that the sign flips the other direction if you multiply or divide by a negative number.Example Solve the inequality.523  xExample Solve the inequality.3274  xxExample Solve the inequality.1235  xExample Solve the inequality.14320 xSolving Nonlinear InequalitiesTo solve inequalities involving squares and other powers of the variable, we use factoringtogether with the following principle:If a product or a quotient has an even number of negative factors, then its value is positive.If a product or a quotient has an odd number of negative factors, then its value is negative.ExampleSolve the inequality 652 xxExampleSolve the inequality 122 xxExampleSolve the inequality    0312 xxxExampleSolve the inequality


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Armstrong MATH 1111 - Inequalities

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