Linear InequalitiesInequalitiesSolving Inequality in One Variable – Symbolic MethodIntersection of Graphs MethodTry It OutX-Intercept MethodNumerical MethodAssignmentCompound InequalityInterval NotationSolving Compound InequalitySlide 12Slide 13Linear RegressionAssignmentsLinear InequalitiesLesson 2.42InequalitiesDefinitionStart with an equation 3x + 5 = 17Replace the equals sign with one ofExamples� < � >2 5 7x + >8 2 3 6x x+ �- +Note that each of these can be changed into the form ax + b § 0where the § is the required inequality symbolNote that each of these can be changed into the form ax + b § 0where the § is the required inequality symbol3Solving Inequality in One Variable – Symbolic MethodTreat inequality in similar manner as an equationAdd same thing to both sides of inequalityMultiply both sides by same positive valueIf negative value used, inequality reversesTry it!Inequality remains same<3 6 9x- + �4Intersection of Graphs MethodGiven f(x) > g(x)Graph both f(x) and g(x)Find the point of intersectionThe solution set includes thex-values where f(x) is above g(x)•f(x)g(x)5Try It OutGivenGraph each side of the equationFind intersectionDecide which side of the intersection matches2 10.5 13.7x x� > -6X-Intercept MethodWrite the inequality as h(x) < 0Graph y = h(x)Solutions occur where graph is below x-axis7Numerical MethodWrite the inequality as h(x) < 0Place h(x) in Y= screenUse Tables (♦Y) and observe values of x where the function is less than 0AssignmentLesson 2.4APage 142Exercises 1 – 73 EOO89 Compound InequalityDefinition:Two inequalities connected by the words and or orExamples5 12x or x� �0 7x and x> �3 1 2x x- � - �Anything in this format should be considered an "and" compound inequalityAnything in this format should be considered an "and" compound inequality10Interval NotationSolution displayed in interval notation [-1, 2)The [ or ] means that the number is included in the intervalThe ( or ) means that the endpoint is not part of the interval[)11 Solving Compound InequalitySymbolicallyAdd the same thing to each partMultiply each part by same positive numberJustify each step in thesequence to the right3 3 6 123 3 61 2xxx� + <- � <- � <12 Solving Compound InequalityGraphicallyGraph all three partsof the inequalities asfunctionsThe solution willbe the values ofx for which the middle function isbetween the other two2 50.2 83xx-< <Try It OutTemp in Fahrenheit x miles above ground level given by T(x) = 85 – 19xUse intersection of graphs todetermine when temp is < 32FWhat does x-intercept on graphy = T(x) represent?13Linear RegressionHome ownership rates given by tableDetermine a linear modeling functionEstimate years when ownership percent was between 58% and 60%Do we interpolate or extrapolate?14x 1900 1950 1980 2006P 47% 55% 64% 69%15AssignmentsLesson 2.4BPage 144Exercises 83 – 99