§ 2.9 Solving Linear Inequalities

Martin-Gay,Beginning Algebra, 5ed2 2 Linear Inequalities in One Variable Alinear inequality in one variableis an inequality that can be written in the form ax+b<c wherea,b, andcare real numbers andais not 0. This definition and all other definitions, properties and steps in this section also hold true for the inequality symbols >,≥, or≤.

Martin-Gay,Beginning Algebra, 5ed3 3 Graphing Solutions to Linear Inequalities • Use a number line. • Use a closed circle at the endpoint of an intervalif you want to include the point. • Use an open circle at the endpoint if you DO NOT want to include the point. 7 Represents the set {xx≤7}. -4 Represents the set {xx> – 4}. Solutions to Linear Inequalities Interval notation, is used to write solution sets of inequalities. • Use a parenthesis if you want to include the number • Use a bracket if you DO NOT want to include the number..

Martin-Gay,Beginning Algebra, 5ed4 4 Solutions to Linear Inequalities x< 3 -5-4-3-2-1012345 –1.5≤x<3 –2< x< 0 -5-4-3-2-1012345 -5-4-3-2-1012345 Interval notation: (–∞, 3) Interval notation: (–2, 0) Interval notation: [–1.5, 3) NOT included Included

Martin-Gay,Beginning Algebra, 5ed5 5 Addition Property of Inequality Ifa,b, andcare real numbers, then a<banda+c<b+c are equivalent

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