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Presents Section 1.3 Inequalities and Absolute Value MB1 Track This section is prepared by M. Zalzali

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1.3 Inequalities and Absolute Value Objectives: 1.Use the notation of inequalities 2.Graph inequalities 3.Use the absolute value notation Fact The set of real numbers is an ordered set. Given any two real numbers, we can determine whether one number is less than, equal to, or greater than the other. Let’s us see how this expressed symbolically: a b a < b is read “a is less than b” if a is to the left of b on the numbered line as we can see below a > b is read “a is greater than b” b” if a is to the right of b on the numbered line as we can see below b a

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… a = b is read “a is equal to b” if a is the same point as b on the numbered line as we can see below a b Example 1 Complete each statement by inserting <, =, > between the given numbers so that the result is true. < < <> > > > > = =

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Graphing an Inequality Suppose we are given an inequality of the form x < - 1. The solution set for this inequality is the set of all values for the variable that makes the inequality a true statement. A convenient way to picture that solution is by a graph on a number line. ) Open interval means –1 is not included Graph the set On the number line Example 2 [ Closed interval means 3 is included

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Class Exercise Graph each set on the number line ( 0.5 Or It can be graphed as 0.5 Open circle means 0.5 is not included

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… Closed circle means 0 is included Or It can be graphed as ]

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Graphing Compound Inequalities Example 3 Graph the set. on the real line Or It can be graphed as )[

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Absolute Value Symbol = An absolute value of a real number is the distance “ on the real line” between the point named by that real number and the origin 0. Hence, Example 4 Evaluate each of the following expressions

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Home Work Do the selected exercises from the syllabus Section 1.3 The end

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