# 1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-1 Equations and Inequalities Chapter 2.

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1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-1 Equations and Inequalities Chapter 2

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-2 2.1 – Solving Linear Equations 2.2 – Problem Solving and Using Formulas 2.3 – Applications of Algebra 2.4 – Additional Application Problems 2.5 – Solving Linear Inequalities 2.6 – Solving Equations and Inequalities Containing Absolute Values Chapter Sections

3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-3 § 2.5 Solving Linear Inequalities

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-4 Solve Inequalities An inequality is a mathematical statement containing one or more inequality sign(, ,  ).

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-5 Properties Used to Solve Inequalities 5.If a > b and c < 0 then ac < bc. For all real numbers a, b, and c: 1.If a > b, then a + c > b + c. 2.If a > b, then a – c > b – c. 3.If a > b and c > 0 then ac > bc. 4.If a > b and c > 0 then. 6. If a > b and c < 0 then.

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-6 Solve the Inequality The solution set is {x|x ≥ -2}. Any real number greater than or equal to -2 will satisfy the inequality.

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-7 Graphing Intervals Endpoints are used to show the end of an interval. A closed circle is used to show that the endpoint is included in the answer. The symbols  and  will use this type of endpoint. An open circle is used to show that the endpoint is NOT included in the answer. The symbols > and < will use this type of endpoint. An arrow is used to show that the interval does not end. -5-4-3-2012345 x  -1

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-8 Graphing Intervals x < 3 -5-4-3-2012345 -1.5  x  3 -2 < x < 0 -5-4-3-2012345-5-4-3-2012345

9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-9 Solving Inequalities Example: Solve the inequality and graph the solution.

10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-10 Solving Inequalities Example continued: Since -1 is always less than or equal to 14, the inequality is true for all real numbers.

11 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-11 Compound Inequalities A compound inequality is formed by joining two inequalities with the word and or or. Examples: 3 < x and x < 5 c  2 and c > -3 x 4 5x – 3  7 or –x + 3 < -5

12 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-12 Solve Compound Inequalities Involving And The solution of a compound inequality using the word and is all the numbers that make both parts of the inequality true. This is the intersection of the solution sets of the two inequalities. Example: 3 < x and x < 5 Find the numbers that satisfy both inequalities. The solution set is the intersection of the two inequalities.

13 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-13 Solve Compound Inequalities Involving And Example: Solve x + 5 ≤ 8 and 2x – 9 > 7. To find the solution algebraically, begin by solving each inequality separately. and

14 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-14 Solve Compound Inequalities Involving And Example continued… Now take the intersection of the sets {x|x ≤ 3} and {x|x > 1}.

15 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-15 Solve Compound Inequalities Involving Or The solution to a compound inequality using the word or is all the numbers that make either of the inequalities a true statement. This is the union of the solution sets of the two inequalities. Example: x > 3 or x < 5 Find the numbers that satisfy at least one of the inequalities. The solution set is the intersection of the two inequalities.