Chapter 2 Linear Equations Section 5 Linear Inequalities

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Chapter 2 Linear Equations Section 5 Linear Inequalities Copyright © 2016, 2012, and 2009

Chapter 2 Linear Equations Section 5 Linear Inequalities Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 1

Study Strategy Study Groups üA Word of Caution/Using Your Calculator Copyright © 2016, 2012,

Study Strategy Study Groups üA Word of Caution/Using Your Calculator Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 2

Concept Linear Inequalities A linear inequality is an inequality containing linear expressions. Copyright ©

Concept Linear Inequalities A linear inequality is an inequality containing linear expressions. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 3

Concept Linear Inequalities Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 4

Concept Linear Inequalities Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 4

Concept Solutions to Inequalities: Number Line The solutions to a linear inequality can be

Concept Solutions to Inequalities: Number Line The solutions to a linear inequality can be represented on a number line. If the endpoint is a solution, we use a closed circle on the number line. If the endpoint is not a solution, we use an open circle. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 5

Example 1 Solutions to Inequalities: Number Line Copyright © 2016, 2012, and 2009 Pearson

Example 1 Solutions to Inequalities: Number Line Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 6

Example 2 Solutions to Inequalities: Number Line Copyright © 2016, 2012, and 2009 Pearson

Example 2 Solutions to Inequalities: Number Line Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 7

Concept Interval Notation Interval notation presents an interval by listing its left and right

Concept Interval Notation Interval notation presents an interval by listing its left and right endpoints. Parentheses are used around endpoints not included in the interval, and square brackets are used if the endpoints are included in the interval. When an interval continues on indefinitely to the right on a number line, we use the symbol in the place of the right endpoint. For intervals that continue on indefinitely to the left on a number line, we use in the place of the left endpoint. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 8

Concept Interval Notation Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 3 9

Concept Interval Notation Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 3 9

Concept 4 Interval Notation Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 10

Concept 4 Interval Notation Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 10

Concept Solving Linear Inequalities Solving a linear inequality is similar to solving a linear

Concept Solving Linear Inequalities Solving a linear inequality is similar to solving a linear equation, with the exception that multiplying or dividing both sides of an inequality by a negative number changes the direction of the inequality. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 11

Example 5 Solving Linear Inequalities Solve Copyright © 2016, 2012, and 2009 Pearson Education,

Example 5 Solving Linear Inequalities Solve Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 12

Example 6 Solving Linear Inequalities Solve Copyright © 2016, 2012, and 2009 Pearson Education,

Example 6 Solving Linear Inequalities Solve Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 13

Concept Compound Inequalities A compound inequality is made up of two or more individual

Concept Compound Inequalities A compound inequality is made up of two or more individual inequalities. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 14

Example 7 Compound Inequalities Solve or or Copyright © 2016, 2012, and 2009 Pearson

Example 7 Compound Inequalities Solve or or Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 15

Example 8 Compound Inequalities Solve Copyright © 2016, 2012, and 2009 Pearson Education, Inc.

Example 8 Compound Inequalities Solve Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 16

Example If a student averages 93 or higher on the five 9 tests given

Example If a student averages 93 or higher on the five 9 tests given in a math class, then the student will earn a grade of A. Narda’s scores on the first four tests are 97, 93, 91, and 89. What score on the fifth test will give Narda an average that is 93 or higher. To find this average, we add five scores and divide by 5. • Let x represent the fifth test. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 17

Example 9 Simplify the numerator. Multiply both sides by 5 to clear the fraction.

Example 9 Simplify the numerator. Multiply both sides by 5 to clear the fraction. Simplify. Narda must score at least a 95 on the fifth test to earn an A. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. Subtract 370 from both sides. 18