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Elementary Algebra

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Elementary AlgebraIndex
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Table of contents
  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Use the Language of Algebra
    4. 1.3 Add and Subtract Integers
    5. 1.4 Multiply and Divide Integers
    6. 1.5 Visualize Fractions
    7. 1.6 Add and Subtract Fractions
    8. 1.7 Decimals
    9. 1.8 The Real Numbers
    10. 1.9 Properties of Real Numbers
    11. 1.10 Systems of Measurement
    12. Chapter Review
      1. Key Terms
      2. Key Concepts
    13. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations and Inequalities
    1. Introduction
    2. 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 2.2 Solve Equations using the Division and Multiplication Properties of Equality
    4. 2.3 Solve Equations with Variables and Constants on Both Sides
    5. 2.4 Use a General Strategy to Solve Linear Equations
    6. 2.5 Solve Equations with Fractions or Decimals
    7. 2.6 Solve a Formula for a Specific Variable
    8. 2.7 Solve Linear Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Math Models
    1. Introduction
    2. 3.1 Use a Problem-Solving Strategy
    3. 3.2 Solve Percent Applications
    4. 3.3 Solve Mixture Applications
    5. 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
    6. 3.5 Solve Uniform Motion Applications
    7. 3.6 Solve Applications with Linear Inequalities
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Graphs
    1. Introduction
    2. 4.1 Use the Rectangular Coordinate System
    3. 4.2 Graph Linear Equations in Two Variables
    4. 4.3 Graph with Intercepts
    5. 4.4 Understand Slope of a Line
    6. 4.5 Use the Slope–Intercept Form of an Equation of a Line
    7. 4.6 Find the Equation of a Line
    8. 4.7 Graphs of Linear Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Systems of Linear Equations
    1. Introduction
    2. 5.1 Solve Systems of Equations by Graphing
    3. 5.2 Solve Systems of Equations by Substitution
    4. 5.3 Solve Systems of Equations by Elimination
    5. 5.4 Solve Applications with Systems of Equations
    6. 5.5 Solve Mixture Applications with Systems of Equations
    7. 5.6 Graphing Systems of Linear Inequalities
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Polynomials
    1. Introduction
    2. 6.1 Add and Subtract Polynomials
    3. 6.2 Use Multiplication Properties of Exponents
    4. 6.3 Multiply Polynomials
    5. 6.4 Special Products
    6. 6.5 Divide Monomials
    7. 6.6 Divide Polynomials
    8. 6.7 Integer Exponents and Scientific Notation
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Factoring
    1. Introduction
    2. 7.1 Greatest Common Factor and Factor by Grouping
    3. 7.2 Factor Quadratic Trinomials with Leading Coefficient 1
    4. 7.3 Factor Quadratic Trinomials with Leading Coefficient Other than 1
    5. 7.4 Factor Special Products
    6. 7.5 General Strategy for Factoring Polynomials
    7. 7.6 Quadratic Equations
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Rational Expressions and Equations
    1. Introduction
    2. 8.1 Simplify Rational Expressions
    3. 8.2 Multiply and Divide Rational Expressions
    4. 8.3 Add and Subtract Rational Expressions with a Common Denominator
    5. 8.4 Add and Subtract Rational Expressions with Unlike Denominators
    6. 8.5 Simplify Complex Rational Expressions
    7. 8.6 Solve Rational Equations
    8. 8.7 Solve Proportion and Similar Figure Applications
    9. 8.8 Solve Uniform Motion and Work Applications
    10. 8.9 Use Direct and Inverse Variation
    11. Chapter Review
      1. Key Terms
      2. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Roots and Radicals
    1. Introduction
    2. 9.1 Simplify and Use Square Roots
    3. 9.2 Simplify Square Roots
    4. 9.3 Add and Subtract Square Roots
    5. 9.4 Multiply Square Roots
    6. 9.5 Divide Square Roots
    7. 9.6 Solve Equations with Square Roots
    8. 9.7 Higher Roots
    9. 9.8 Rational Exponents
    10. Chapter Review
      1. Key Terms
      2. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Quadratic Equations
    1. Introduction
    2. 10.1 Solve Quadratic Equations Using the Square Root Property
    3. 10.2 Solve Quadratic Equations by Completing the Square
    4. 10.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 10.4 Solve Applications Modeled by Quadratic Equations
    6. 10.5 Graphing Quadratic Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  12. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
  13. Index
A
absolute value 1.3 Add and Subtract Integers, 1.3 Add and Subtract Integers
addition 1.2 Use the Language of Algebra
Addition Property of Equality 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality, 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
additive identity 1.9 Properties of Real Numbers
additive inverse 1.9 Properties of Real Numbers
amount of discount 3.2 Solve Percent Applications
an inconsistent system 5.1 Solve Systems of Equations by Graphing
area 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem, 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
associative property 1.9 Properties of Real Numbers, 1.9 Properties of Real Numbers
axis of symmetry 10.5 Graphing Quadratic Equations, 10.5 Graphing Quadratic Equations
B
binomial 6.1 Add and Subtract Polynomials, 6.3 Multiply Polynomials, 6.3 Multiply Polynomials, 6.3 Multiply Polynomials, 6.4 Special Products, 6.4 Special Products, 6.6 Divide Polynomials
boundary line 4.7 Graphs of Linear Inequalities, 4.7 Graphs of Linear Inequalities
C
coefficient 1.2 Use the Language of Algebra
coincident lines 5.1 Solve Systems of Equations by Graphing
commutative property 1.9 Properties of Real Numbers
complementary angles 5.4 Solve Applications with Systems of Equations
completing the square 10.2 Solve Quadratic Equations by Completing the Square
complex fraction 1.5 Visualize Fractions
complex rational expression 8.5 Simplify Complex Rational Expressions, 8.5 Simplify Complex Rational Expressions
composite number 1.1 Introduction to Whole Numbers
conditional equation 2.4 Use a General Strategy to Solve Linear Equations
conjugate pair 6.4 Special Products
consecutive even integers 10.4 Solve Applications Modeled by Quadratic Equations, 10.4 Solve Applications Modeled by Quadratic Equations
consecutive odd integers 10.4 Solve Applications Modeled by Quadratic Equations, 10.4 Solve Applications Modeled by Quadratic Equations
consistent system 5.1 Solve Systems of Equations by Graphing, 5.1 Solve Systems of Equations by Graphing
constant 1.2 Use the Language of Algebra, 1.2 Use the Language of Algebra
contradiction 2.4 Use a General Strategy to Solve Linear Equations, 2.4 Use a General Strategy to Solve Linear Equations
counting number 1.1 Introduction to Whole Numbers
counting numbers 1.8 The Real Numbers
D
decimal 1.7 Decimals, 1.7 Decimals, 1.7 Decimals, 1.7 Decimals
degree of a constant 6.1 Add and Subtract Polynomials
degree of a polynomial 6.1 Add and Subtract Polynomials
degree of a term 6.1 Add and Subtract Polynomials
denominator 1.1 Introduction to Whole Numbers, 1.5 Visualize Fractions, 1.6 Add and Subtract Fractions
dependent 5.1 Solve Systems of Equations by Graphing
dependent equations 5.1 Solve Systems of Equations by Graphing
difference of squares 7.4 Factor Special Products
discount rate 3.2 Solve Percent Applications, 3.2 Solve Percent Applications
discriminant 10.3 Solve Quadratic Equations Using the Quadratic Formula, 10.3 Solve Quadratic Equations Using the Quadratic Formula
distributive property 1.9 Properties of Real Numbers, 1.9 Properties of Real Numbers
divisible 1.1 Introduction to Whole Numbers
division 1.2 Use the Language of Algebra, 1.4 Multiply and Divide Integers, 1.4 Multiply and Divide Integers, 1.5 Visualize Fractions, 1.5 Visualize Fractions, 1.6 Add and Subtract Fractions, 1.7 Decimals, 1.9 Properties of Real Numbers, 1.9 Properties of Real Numbers
Division Property of Equality 2.2 Solve Equations using the Division and Multiplication Properties of Equality, 2.2 Solve Equations using the Division and Multiplication Properties of Equality
E
elapsed time 3.5 Solve Uniform Motion Applications
Elimination Method 5.3 Solve Systems of Equations by Elimination
equal sign 1.2 Use the Language of Algebra, 1.2 Use the Language of Algebra, 1.2 Use the Language of Algebra
equals sign 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
equation 1.2 Use the Language of Algebra
equivalent decimals 1.8 The Real Numbers
equivalent fractions 1.5 Visualize Fractions
evaluate an expression 1.2 Use the Language of Algebra
expression 1.2 Use the Language of Algebra, 1.9 Properties of Real Numbers
extraneous solution to a rational equation 8.6 Solve Rational Equations
F
factoring 7.1 Greatest Common Factor and Factor by Grouping
factors 1.1 Introduction to Whole Numbers, 1.1 Introduction to Whole Numbers, 1.10 Systems of Measurement
fraction 1.7 Decimals, 1.8 The Real Numbers
fraction bar 1.5 Visualize Fractions
fraction operations 1.6 Add and Subtract Fractions
G
geoboard 4.4 Understand Slope of a Line, 4.4 Understand Slope of a Line
graph of a linear equation 4.2 Graph Linear Equations in Two Variables
greatest common factor 7.1 Greatest Common Factor and Factor by Grouping, 7.1 Greatest Common Factor and Factor by Grouping
grouping symbols 1.2 Use the Language of Algebra
H
horizontal line 4.2 Graph Linear Equations in Two Variables
I
identity 2.4 Use a General Strategy to Solve Linear Equations, 2.4 Use a General Strategy to Solve Linear Equations
Identity Property of Addition 1.9 Properties of Real Numbers
Identity Property of Multiplication 1.9 Properties of Real Numbers
improper fractions 1.8 The Real Numbers
inconsistent system 5.1 Solve Systems of Equations by Graphing
independent 5.1 Solve Systems of Equations by Graphing
independent equations 5.1 Solve Systems of Equations by Graphing
index 9.7 Higher Roots
integers 1.3 Add and Subtract Integers, 1.4 Multiply and Divide Integers, 1.8 The Real Numbers
intercepts of a line 4.3 Graph with Intercepts
interest 3.2 Solve Percent Applications
interval notation 2.7 Solve Linear Inequalities
Inverse Property of Addition 1.9 Properties of Real Numbers
Inverse Property of Multiplication 1.9 Properties of Real Numbers
irrational 1.8 The Real Numbers
irrational number 1.8 The Real Numbers
L
least common denominator 1.6 Add and Subtract Fractions
least common multiple 1.1 Introduction to Whole Numbers, 1.1 Introduction to Whole Numbers
like radicals 9.3 Add and Subtract Square Roots, 9.7 Higher Roots, 9.7 Higher Roots
like square roots 9.3 Add and Subtract Square Roots, 9.4 Multiply Square Roots
like terms 1.2 Use the Language of Algebra
linear equation 4.1 Use the Rectangular Coordinate System, 4.1 Use the Rectangular Coordinate System
linear inequality 4.7 Graphs of Linear Inequalities, 4.7 Graphs of Linear Inequalities
list price 3.2 Solve Percent Applications
M
mark-up 3.2 Solve Percent Applications
metric system 1.10 Systems of Measurement
mixture problems 3.3 Solve Mixture Applications
monomial 6.1 Add and Subtract Polynomials, 6.1 Add and Subtract Polynomials, 6.2 Use Multiplication Properties of Exponents, 6.3 Multiply Polynomials, 6.3 Multiply Polynomials, 6.6 Divide Polynomials, 6.6 Divide Polynomials
multiples 1.1 Introduction to Whole Numbers
multiplication 1.2 Use the Language of Algebra, 1.4 Multiply and Divide Integers, 1.4 Multiply and Divide Integers
Multiplication Property of Equality 2.2 Solve Equations using the Division and Multiplication Properties of Equality
multiplicative identity 1.9 Properties of Real Numbers
multiplicative inverse 1.9 Properties of Real Numbers
multiplying fractions 1.5 Visualize Fractions
N
negative exponent 6.7 Integer Exponents and Scientific Notation, 6.7 Integer Exponents and Scientific Notation
negative numbers 1.3 Add and Subtract Integers
negative slope 4.4 Understand Slope of a Line
neutral pairs 1.3 Add and Subtract Integers
nth root of a number 9.7 Higher Roots
number line 1.1 Introduction to Whole Numbers, 1.3 Add and Subtract Integers, 1.8 The Real Numbers
number system 1.1 Introduction to Whole Numbers
numerator 1.5 Visualize Fractions
O
operations 1.2 Use the Language of Algebra
opposite 1.3 Add and Subtract Integers
Order of Operations 1.2 Use the Language of Algebra
ordered pair 4.1 Use the Rectangular Coordinate System, 4.1 Use the Rectangular Coordinate System, 4.1 Use the Rectangular Coordinate System, 4.1 Use the Rectangular Coordinate System
origin 4.1 Use the Rectangular Coordinate System, 4.1 Use the Rectangular Coordinate System
original cost 3.2 Solve Percent Applications
P
parabola 10.5 Graphing Quadratic Equations, 10.5 Graphing Quadratic Equations
parallel lines 4.5 Use the Slope–Intercept Form of an Equation of a Line
percent 1.7 Decimals, 3.2 Solve Percent Applications
percent decrease 3.2 Solve Percent Applications
percent increase 3.2 Solve Percent Applications
perfect square trinomials pattern 7.4 Factor Special Products
perimeter 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem, 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
perpendicular 4.5 Use the Slope–Intercept Form of an Equation of a Line
perpendicular lines 4.5 Use the Slope–Intercept Form of an Equation of a Line
place values 1.1 Introduction to Whole Numbers, 1.7 Decimals, 1.7 Decimals
point–slope form 4.6 Find the Equation of a Line
point–slope method 4.4 Understand Slope of a Line
polynomial 6.1 Add and Subtract Polynomials, 6.1 Add and Subtract Polynomials
positive slope 4.4 Understand Slope of a Line
prime factorization 1.1 Introduction to Whole Numbers, 1.1 Introduction to Whole Numbers
prime number 1.1 Introduction to Whole Numbers, 1.1 Introduction to Whole Numbers, 1.5 Visualize Fractions
principal 3.2 Solve Percent Applications
principal nth root 9.7 Higher Roots
principal square root 1.8 The Real Numbers, 9.7 Higher Roots
product 1.1 Introduction to Whole Numbers, 1.1 Introduction to Whole Numbers, 1.4 Multiply and Divide Integers, 1.5 Visualize Fractions, 1.5 Visualize Fractions, 1.7 Decimals, 1.9 Properties of Real Numbers
profit 3.6 Solve Applications with Linear Inequalities
proper fractions 1.7 Decimals, 1.8 The Real Numbers
proportion 8.7 Solve Proportion and Similar Figure Applications, 8.7 Solve Proportion and Similar Figure Applications
Pythagorean Theorem 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
Q
quadrant 4.1 Use the Rectangular Coordinate System
quadratic equation 10.1 Solve Quadratic Equations Using the Square Root Property
quadratic equation in two variables 10.5 Graphing Quadratic Equations, 10.5 Graphing Quadratic Equations
quadratic equations 7.6 Quadratic Equations
quotient 1.4 Multiply and Divide Integers, 1.5 Visualize Fractions
R
radical equation 9.6 Solve Equations with Square Roots, 9.6 Solve Equations with Square Roots
radical sign 1.8 The Real Numbers
rate of interest 3.2 Solve Percent Applications
ratio 1.5 Visualize Fractions
rational equation 8.6 Solve Rational Equations, 8.6 Solve Rational Equations
rational exponents 9.8 Rational Exponents, 9.8 Rational Exponents
rational expression 8.1 Simplify Rational Expressions, 8.1 Simplify Rational Expressions
rational number 1.8 The Real Numbers
rationalize 10.1 Solve Quadratic Equations Using the Square Root Property
rationalizing the denominator 9.5 Divide Square Roots
real number 1.8 The Real Numbers
reciprocal 1.5 Visualize Fractions, 1.9 Properties of Real Numbers
rectangle 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
rectangular coordinate system 4.1 Use the Rectangular Coordinate System, 4.1 Use the Rectangular Coordinate System
repeating decimal 1.7 Decimals
right triangle 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
rise 4.4 Understand Slope of a Line, 4.4 Understand Slope of a Line
rounding 1.1 Introduction to Whole Numbers
run 4.4 Understand Slope of a Line, 4.4 Understand Slope of a Line
S
scientific notation 6.7 Integer Exponents and Scientific Notation, 6.7 Integer Exponents and Scientific Notation
similar figures 8.7 Solve Proportion and Similar Figure Applications, 8.7 Solve Proportion and Similar Figure Applications
simple interest 3.2 Solve Percent Applications, 3.3 Solve Mixture Applications
simplification 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
simplified 1.5 Visualize Fractions
simplify an expression 1.2 Use the Language of Algebra
slope formula 4.4 Understand Slope of a Line, 4.4 Understand Slope of a Line
slope of a line 4.4 Understand Slope of a Line
slope–intercept form 4.5 Use the Slope–Intercept Form of an Equation of a Line
solution of a linear inequality 4.7 Graphs of Linear Inequalities
solution of an equation 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
solutions to a system of equations 5.1 Solve Systems of Equations by Graphing
square 1.8 The Real Numbers
square root 1.8 The Real Numbers
Square Root Property 10.1 Solve Quadratic Equations Using the Square Root Property, 10.1 Solve Quadratic Equations Using the Square Root Property
standard form 6.1 Add and Subtract Polynomials
subtraction 1.2 Use the Language of Algebra
subtraction property 1.3 Add and Subtract Integers
Subtraction Property of Equality 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality, 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
sum and difference of cubes pattern 7.4 Factor Special Products
supplementary angles 5.4 Solve Applications with Systems of Equations
system of linear inequalities 5.6 Graphing Systems of Linear Inequalities
systems of linear equations 5.1 Solve Systems of Equations by Graphing
T
term 1.2 Use the Language of Algebra
trinomial 6.1 Add and Subtract Polynomials, 6.3 Multiply Polynomials, 6.3 Multiply Polynomials, 6.3 Multiply Polynomials, 6.4 Special Products, 6.6 Divide Polynomials
U
U.S. system 1.10 Systems of Measurement
V
variable 1.2 Use the Language of Algebra, 1.2 Use the Language of Algebra, 1.3 Add and Subtract Integers
variables 2.3 Solve Equations with Variables and Constants on Both Sides
vertex 10.5 Graphing Quadratic Equations, 10.5 Graphing Quadratic Equations
vertical line 4.2 Graph Linear Equations in Two Variables
vertices 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
W
whole number 1.1 Introduction to Whole Numbers
whole numbers 1.8 The Real Numbers
X
x- intercept 4.3 Graph with Intercepts
x- intercept of a line 4.3 Graph with Intercepts
x-coordinate 4.1 Use the Rectangular Coordinate System, 4.1 Use the Rectangular Coordinate System
x-intercept 10.5 Graphing Quadratic Equations
x-intercepts of a parabola 10.5 Graphing Quadratic Equations
Y
y- intercept 4.3 Graph with Intercepts
y- intercept of a line 4.3 Graph with Intercepts
y-coordinate 4.1 Use the Rectangular Coordinate System, 4.1 Use the Rectangular Coordinate System
y-intercept 10.5 Graphing Quadratic Equations
Z
Zero Product Property 7.6 Quadratic Equations, 7.6 Quadratic Equations
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