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Finish the excel spreadsheet and read the chapter. Show all the work so I can get the full points. Show work and then add in answer. Must be good at algebra. Finish the excel spreadsheet and read the chapter. Show all the work so I can get the full points. Show work and then add in answer. Must be good at algebra. Finish the excel spreadsheet and read the chapter. Show all the work so I can get the full points. Show work and then add in answer. Must be good at algebra. Finish the excel spreadsheet and read the chapter. Show all the work so I can get the full points. Show work and then add in answer. Must be good at algebra. algebra_i_for_the_community_college_1.pdf mat220_week1_assignment_with_video_links___updated_083018.xlsx Unformatted Attachment Preview Algebra I for the Community College Collection Editor: Ann Simao Algebra I for the Community College Collection Editor: Ann Simao Authors: Denny Burzynski Wade Ellis Online: < http://legacy.cnx.org/content/col11598/1.3/ > OpenStax-CNX This selection and arrangement of content as a collection is copyrighted by Ann Simao. It is licensed under the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). Collection structure revised: December 19, 2014 PDF generated: December 19, 2014 For copyright and attribution information for the modules contained in this collection, see p. 327. Table of Contents 1 Chapter 1: Introduction to Real Numbers and Algebraic Expressions 1.1 1.2 2 Chapter 2: Solving Linear Equations and Inequalities 2.1 2.2 3 Chapter 3: Graphing Linear Equations and Inequalities 3.1 3.2 4 Chapter 4: Solving Systems of Linear Equations 4.1 4.2 4.3 5 Chapter 5: Exponents and Polynomials 5.1 5.2 Index Attributions Chapter 1 Part A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Chapter 1 Part B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Chapter 2 Part A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Chapter 2 Part B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Chapter 3 Part A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Chapter 3 Part B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 156 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 Solving Systems of Linear Equations by Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Solving Systems of Linear Equations by Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 Introduction to Systems of Linear Equations: Solving by Graphing . . . . . . . . . . . . . . . . . . . . . . . . 239 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 Chapter 5 Part X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Chapter 5 Part Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 iv Available for free at Connexions Chapter 1 Chapter 1: Introduction to Real Numbers and Algebraic Expressions 1.1 Chapter 1 Part A 1 1.1.1 Real Numbers 1.1.1.1 Section Overview • • • • Positive and Negative Numbers Reading Signed Numbers Opposites The Double-Negative Property 1.1.1.2 Positive and Negative Numbers Positive and Negative Numbers sign number + and − Notation positive negative Each real number other than zero has a negative associated with it. A real number is said to be a if it is to the right of 0 on the number line and positive if it is to the left of 0 on the number line. note: A number is denoted as A number is denoted as if it is directly preceded by a plus sign or no sign at all. if it is directly preceded by a minus sign. 1.1.1.3 Reading Signed Numbers The plus and minus signs now have two meanings : The plus sign can denote the operation of addition or a positive number. The minus sign can denote the operation of subtraction or a negative number. To avoid any confusion between sign and operation, it is preferable to read the sign of a number as positive or negative. When + is used as an operation sign, it is read as plus. When − is used as an operation sign, it is read as minus. 1 This content is available online at . Available for free at Connexions 1 CHAPTER 1. 2 CHAPTER 1: INTRODUCTION TO REAL NUMBERS AND ALGEBRAIC EXPRESSIONS 1.1.1.3.1 Sample Set A Read each expression so as to avoid confusion between operation and sign. Example 1.1 −8 Example 1.2 + (−2) Example 1.3 should be read as negative eight rather than minus eight. 4 should be read as four plus negative two rather than four plus minus two. −6 + (−3)should be read as negative six plus negative three rather than minus six plus minus three. Example 1.4 −15−(−6)should be read as negative fteen minus negative six rather than minus fteen minus minus six. Example 1.5 −5 + Example 1.6 7 should be read as negative ve plus seven rather than minus ve plus seven. 0−2 should be read as zero minus two. 1.1.1.3.2 Practice Set A Exercise 1.1.1.1 + Exercise 1.1.1.2 2 + (−8) Exercise 1.1.1.3 −7 + 5 Exercise 1.1.1.4 −10 − (+3) Exercise 1.1.1.5 −1 − (−8) Exercise 1.1.1.6 Write each expression in words. 6 0 (Solution on p. 60.) 1 (Solution on p. 60.) (Solution on p. 60.) (Solution on p. 60.) (Solution on p. 60.) (Solution on p. 60.) + (−11) 1.1.1.4 Opposites Opposites Opposites On the number line, each real number, other than zero, has an image on the opposite side of 0. For this reason, we say that each real number has an opposite. opposite signs. are the same distance from zero but have The opposite of a real number is denoted by placing a negative sign directly in front of the number. Thus, if a is any real number, then −a is its opposite. note: The letter a is a variable. Thus, a need not be positive, and −a need not be negative. Available for free at Connexions 3 If a is any real number, −a is opposite a on the number line. 1.1.1.5 The Double-Negative Property The number a is opposite −a on the number line. Therefore, − (−a) is opposite −a on the number line. This means that − (−a) = a Double-Negative Property: − (−a) = a From this property of opposites, we can suggest the double-negative property for real numbers. a is a real − (−a) = a If number, then 1.1.1.5.1 Sample Set B Find the opposite of each number. Example 1.7 If a= 2, then Example 1.8 If a = −4, −a = −2. then Also, − (−a) = − (−2) = 2. −a = − (−4) = 4. 1.1.1.5.2 Practice Set B Exercise 1.1.1.7 Exercise 1.1.1.8 Exercise 1.1.1.9 Exercise 1.1.1.10 Exercise 1.1.1.11 Exercise 1.1.1.12 − [− (−7)] Exercise 1.1.1.13 Also, − (−a) = a = − 4. Find the opposite of each number. (Solution on p. 60.) 8 (Solution on p. 60.) 17 (Solution on p. 60.) -6 (Solution on p. 60.) -15 (Solution on p. 60.) -(-1) Suppose a is a positive number. Is (Solution on p. 60.) (Solution on p. 60.) −a positive or negative? Available for free at Connexions CHAPTER 1. 4 Exercise 1.1.1.14 a Exercise 1.1.1.15 Suppose is a negative number. Is CHAPTER 1: INTRODUCTION TO REAL NUMBERS AND ALGEBRAIC EXPRESSIONS (Solution on p. 60.) −a positive or negative? Suppose we do not know the sign of the number (Solution on p. 60.) k. Is −k positive, negative, or do we not know? 1.1.1.6 Exercises Exercise 1.1.1.16 Exercise 1.1.1.17 A number is denoted as positive if it is directly preceded by A number is denoted as negative if it is directly preceded by Exercise 1.1.1.18 −7 Exercise 1.1.1.19 −5 Exercise 1.1.1.20 Exercise 1.1.1.21 Exercise 1.1.1.22 − (−1) Exercise 1.1.1.23 (Solution on p. 60.) . . How should the number in the following 6 problems be read? (Write in words.) (Solution on p. 60.) (Solution on p. 60.) 15 11 (Solution on p. 60.) − (−5) Exercise 1.1.1.24 5+3 Exercise 1.1.1.25 3+8 Exercise 1.1.1.26 + (−3) Exercise 1.1.1.27 1 + (−9) Exercise 1.1.1.28 −7 − (−2) Exercise 1.1.1.29 For the following 6 problems, write each expression in words. (Solution on p. 60.) (Solution on p. 60.) 15 (Solution on p. 60.) 0 − (−12) Exercise 1.1.1.30 − (−2) Exercise 1.1.1.31 − (− ) Exercise 1.1.1.32 For the following 6 problems, rewrite each number in simpler form. (Solution on p. 60.) 16 (Solution on p. 60.) − [− (−8)] Available for free at Connexions 5 Exercise 1.1.1.33 − [− (− )] Exercise 1.1.1.34 7 − (−3) Exercise 1.1.1.35 20 (Solution on p. 60.) 6 − (−4) 1.1.1.6.1 Exercises for Review Exercise 1.1.1.36 8÷ Exercise 1.1.1.37 Exercise 1.1.1.38 Exercise 1.1.1.39 Exercise 1.1.1.40 2 ( here ) Find the quotient; 3 ( here ) Solve the proportion: (Solution on p. 60.) 27. 5 9 = 60 x 4 ( here ) Use the method of rounding to estimate the sum: 5829 (Solution on p. 61.) + 8767 5 ( here ) Use a unit fraction to convert 4 yd to feet. (Solution on p. 61.) 6 ( here ) Convert 25 cm to hm. 7 1.1.2 Real Number Line 1.1.2.1 Overview • • • The Real Number Line The Real Numbers Ordering the Real Numbers 1.1.2.2 The Real Number Line Real Number Line visually In our study of algebra, we will use several collections of numbers. display the numbers in which we are interested. The real number line allows us to A line is composed of innitely many points. To each point we can associate a unique number, and with Coordinate Graph each number we can associate a particular point. The number associated with a point on the number line is called the coordinate graph The point on a line that is associated with a particular number is called the Construction of the Real Number Line We construct the real number line as follows: of the point. of that number. 2 Decimals: Division of Decimals 3 Ratios and Rates: Proportions 4 Techniques of Estimation: Estimation by Rounding 5 Measurement and Geometry: Measurement and the United States System 6 Measurement and Geometry: The Metric System of Measurement 7 This content is available online at . Available for free at Connexions CHAPTER 1. 6 CHAPTER 1: INTRODUCTION TO REAL NUMBERS AND ALGEBRAIC EXPRESSIONS 1. Draw a horizontal line. 2. Choose any point on the line and label it 0. This point is called the origin . 3. Choose a convenient length. This length is called 1 unit. Starting at 0, mark this length o in both directions, being careful to have the lengths look like they are about the same. We now dene a real number. Real Number real number Positive and Negative Real Numbers A is any number that is the coordinate of a point on the real number line. collection of real numbers positive real numbers negative real numbers The collection of these innitely many numbers is called the . The real numbers whose graphs are to the right of 0 are called the appear to the left of 0 are called the . The real numbers whose graphs . The number 0 is neither positive nor negative. 1.1.2.3 The Real Numbers The collection of real numbers has many subcollections. The subcollections that are of most interest to us Natural Numbers natural numbers (N ): {1, 2, 3, . . . } are listed below along with their notations and graphs. The Whole Numbers whole numbers (W ): {0, 1, 2, 3, . . . } The Integers integers (Z): {. . . , − 3, − 2, −1, 0, 1, 2, 3, . . . } Notice that every natural number is a whole number. The Rational Numbers rational numbers (Q): a b b 6= 0 Fractions Notice that every whole number is an integer. The and Rational numbers are real numbers that can be written in the form are integers, and . Rational numbers are commonly called fractions. Available for free at Connexions a/b, where 7 Division by 1 b Division by 0 Since can equal 1, every integer is a rational number: Recall that 10/2 = 5 since 2 · 5 = 10. However, if a 1 = a. 10/0 = x, then 0 · x = 10. But 0 · x = 0, not 10. This suggests that no quotient exists. 0/0 = x. If 0/0 = x, then 0 · x = 0. But this means that x could be any number, that 0 · 4 = 0, or 0/0 = 28 since 0 · 28 = 0. This suggests that the quotient is indeterminant. Now consider Is Undened or Indeterminant 0/0 = 4 x/0 since is, Division by 0 is undened or indeterminant. Do not divide by 0. Rational numbers have decimal representations that either terminate or do not terminate but contain a repeating block of digits. Some examples are: 3 = 0.75 |4 {z } Terminating 15 = 1.36363636 . . . |11 {z } Nonterminating, but repeating Some rational numbers are graphed below. Irrational Numbers irrational numbers (Ir): The Irrational numbers are numbers that cannot be written as the quotient of two integers. They are numbers whose decimal representations are nonterminating and nonrepeating. Some examples are 4.01001000100001 . . . π = 3.1415927 . . . Notice that the collections of rational numbers and irrational numbers have no numbers in common. When graphed on the number line, the rational and irrational numbers account for every point on the number line. Thus each point on the number line has a coordinate that is either a rational or an irrational number. In summary, we have 1.1.2.4 Sample Set A The summaray chart illustrates that Example 1.9 Every natural number is a real number. Available for free at Connexions CHAPTER 1. 8 CHAPTER 1: INTRODUCTION TO REAL NUMBERS AND ALGEBRAIC EXPRESSIONS Example 1.10 Example 1.11 Every whole number is a real number. No integer is an irrational number. 1.1.2.5 Practice Set A Exercise 1.1.2.1 Exercise 1.1.2.2 Exercise 1.1.2.3 Exercise 1.1.2.4 Exercise 1.1.2.5 Exercise 1.1.2.6 (Solution on p. 61.) Is every natural number a whole number? (Solution on p. 61.) Is every whole number an integer? (Solution on p. 61.) Is every integer a rational number? (Solution on p. 61.) Is every rational number a real number? (Solution on p. 61.) Is every integer a natural number? (Solution on p. 61.) Is there an integer that is a natural number? 1.1.2.6 Ordering the Real Numbers Ordering the Real Numbers A real number of the graph of b is said to be greater a on the number line. than a real number a, denoted b > a, if the graph of b is to the right 1.1.2.7 Sample Set B As we would expect, the right of −5 5>2 since 5 is to the right of 2 on the number line. Also, −2 > − 5 since −2 on the number line. 1.1.2.8 Practice Set B Exercise 1.1.2.7 Exercise 1.1.2.8 Exercise 1.1.2.9 Exercise 1.1.2.10 Exercise 1.1.2.11 (Solution on p. 61.) Are all positive numbers greater than 0? (Solution on p. 61.) Are all positive numbers greater than all negative numbers? (Solution on p. 61.) Is 0 greater than all negative numbers? (Solution on p. 61.) Is there a largest positive number? Is there a smallest negative number? (Solution on p. 61.) How many real numbers are there? How many real numbers are there between 0 and 1? Available for free at Connexions is to 9 1.1.2.9 Sample Set C Example 1.12 What integers can replace x so that the following statement is true? −4 ≤ x < 2 This statement indicates that the number represented by −4 is less than or equal to x, and at the same time, x x is between −4 and 2. Specically, is strictly less than 2. This statement is an example of a compound inequality. The integers are Example 1.13 −4, − 3, − 2, − 1, 0, 1. Draw a number line that extends from including −2 −3 to 7. Place points at all whole numbers between and and 6. Example 1.14 Draw a number line that extends from −4 to 6 and place points at all real numbers greater than or equal to 3 but strictly less than 5. open circle It is customary to use a closed circle to indicate that a point is included in the graph and an to indicate that a point is not included. 1.1.2.10 Practice Set C Exercise 1.1.2.12 What whole numbers can replace (Solution on p. 61.) x so that the following statement is true? −3 ≤ x < 3 Exercise 1.1.2.13 Draw a number line that extends from equal to −4 (Solution on p. 61.) −5 to 3 and place points at all numbers greater than or but strictly less than 2. Available for free at Connexions CHAPTER 1. 10 CHAPTER 1: INTRODUCTION TO REAL NUMBERS AND ALGEBRAIC EXPRESSIONS 1.1.2.11 Exercises For the following problems, next to each real number, note all collections to which it belongs by writing for natural numbers, and R W for whole numbers, Z for integers, Q for rational numbers, Ir Exercise 1.1.2.14 Exercise 1.1.2.15 −12 Exercise 1.1.2.16 Exercise 1.1.2.17 −24 Exercise 1.1.2.18 86.3333 . . . Exercise 1.1.2.19 49.125125125 . . . Exercise 1.1.2.20 N for irrational numbers, for real numbers. Some numbers may require more than one letter. (Solution on p. 61.) 1 2 (Solution on p. 61.) 0 7 8 (Solution on p. 61.) (Solution on p. 61.) −15.07 For the following problems, draw a number line that extends from −3 Exercise 1.1.2.21 1 Exercise 1.1.2.22 −2 Exercise 1.1.2.23 − Exercise 1.1.2.24 Exercise 1.1.2.25 to 3. Locate each real number on the number line by placing a point (closed circle) at its approximate location. 1 2 (Solution on p. 61.) 1 8 (Solution on p. 61.) Is 0 a positive number, negative number, neither, or both? An integer is an even integer if it can be divided by 2 without a remainder; otherwise the number is odd. Draw a number line that extends from Exercise 1.1.2.26 −5 to 5 and place points at all negative even integers and at all positive odd integers. Draw a number line that extends from −3 (Solution on p. 61.) −5 to 5. Place points at all integers strictly greater than but strictly less than 4. For the following problems, draw a number line that extends from Exercise 1.1.2.27 −5 −2 Exercise 1.1.2.28 −3 Exercise 1.1.2.29 −4 Exercise 1.1.2.30 −5 to 5. Place points at all real numbers between and including each pair of numbers. and (Solution on p. 61.) and 4 and 0 Draw a number line that extends ... Purchase answer to see full attachment