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.5xd.1xExampleWrite 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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