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Elementary Algebra

Index

Elementary AlgebraIndex
  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. Key Terms
    13. Key Concepts
    14. 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. Key Terms
    10. Key Concepts
    11. 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. Key Terms
    9. Key Concepts
    10. 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. Key Terms
    10. Key Concepts
    11. 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. Key Terms
    9. Key Concepts
    10. 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. Key Terms
    10. Key Concepts
    11. 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. Key Terms
    9. Key Concepts
    10. 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. Key Terms
    12. Key Concepts
    13. 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. Key Terms
    11. Key Concepts
    12. 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. Key Terms
    8. Key Concepts
    9. 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 value1.3 Add and Subtract Integers, 1.3 Add and Subtract Integers
addition1.2 Use the Language of Algebra
Addition Property of Equality2.1 Solve Equations Using the Subtraction and Addition Properties of Equality, 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
additive identity1.9 Properties of Real Numbers
additive inverse1.9 Properties of Real Numbers
amount of discount3.2 Solve Percent Applications
an inconsistent system5.1 Solve Systems of Equations by Graphing
area3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem, 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
associative property1.9 Properties of Real Numbers, 1.9 Properties of Real Numbers
axis of symmetry10.5 Graphing Quadratic Equations, 10.5 Graphing Quadratic Equations
B
binomial6.1 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 line4.7 Graphs of Linear Inequalities, 4.7 Graphs of Linear Inequalities
C
coefficient1.2 Use the Language of Algebra
coincident lines5.1 Solve Systems of Equations by Graphing
commutative property1.9 Properties of Real Numbers
complementary angles5.4 Solve Applications with Systems of Equations
completing the square10.2 Solve Quadratic Equations by Completing the Square
complex fraction1.5 Visualize Fractions
complex rational expression8.5 Simplify Complex Rational Expressions, 8.5 Simplify Complex Rational Expressions
composite number1.1 Introduction to Whole Numbers
conditional equation2.4 Use a General Strategy to Solve Linear Equations
conjugate pair6.4 Special Products
consecutive even integers10.4 Solve Applications Modeled by Quadratic Equations, 10.4 Solve Applications Modeled by Quadratic Equations
consecutive odd integers10.4 Solve Applications Modeled by Quadratic Equations, 10.4 Solve Applications Modeled by Quadratic Equations
consistent system5.1 Solve Systems of Equations by Graphing, 5.1 Solve Systems of Equations by Graphing
constant1.2 Use the Language of Algebra, 1.2 Use the Language of Algebra
contradiction2.4 Use a General Strategy to Solve Linear Equations, 2.4 Use a General Strategy to Solve Linear Equations
counting number1.1 Introduction to Whole Numbers
counting numbers1.8 The Real Numbers
D
decimal1.7 Decimals, 1.7 Decimals, 1.7 Decimals, 1.7 Decimals
degree of a constant6.1 Add and Subtract Polynomials
degree of a polynomial6.1 Add and Subtract Polynomials
degree of a term6.1 Add and Subtract Polynomials
denominator1.1 Introduction to Whole Numbers, 1.5 Visualize Fractions, 1.6 Add and Subtract Fractions
dependent5.1 Solve Systems of Equations by Graphing
dependent equations5.1 Solve Systems of Equations by Graphing
difference of squares7.4 Factor Special Products
discount rate3.2 Solve Percent Applications, 3.2 Solve Percent Applications
discriminant10.3 Solve Quadratic Equations Using the Quadratic Formula, 10.3 Solve Quadratic Equations Using the Quadratic Formula
distributive property1.9 Properties of Real Numbers, 1.9 Properties of Real Numbers
divisible1.1 Introduction to Whole Numbers
division1.2 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 Equality2.2 Solve Equations using the Division and Multiplication Properties of Equality, 2.2 Solve Equations using the Division and Multiplication Properties of Equality
E
elapsed time3.5 Solve Uniform Motion Applications
Elimination Method5.3 Solve Systems of Equations by Elimination
equal sign1.2 Use the Language of Algebra, 1.2 Use the Language of Algebra, 1.2 Use the Language of Algebra
equals sign2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
equation1.2 Use the Language of Algebra
equivalent decimals1.8 The Real Numbers
equivalent fractions1.5 Visualize Fractions
evaluate an expression1.2 Use the Language of Algebra
expression1.2 Use the Language of Algebra, 1.9 Properties of Real Numbers
extraneous solution to a rational equation8.6 Solve Rational Equations
F
factoring7.1 Greatest Common Factor and Factor by Grouping
factors1.1 Introduction to Whole Numbers, 1.1 Introduction to Whole Numbers, 1.10 Systems of Measurement
fraction1.7 Decimals, 1.8 The Real Numbers
fraction bar1.5 Visualize Fractions
fraction operations1.6 Add and Subtract Fractions
G
geoboard4.4 Understand Slope of a Line, 4.4 Understand Slope of a Line
graph of a linear equation4.2 Graph Linear Equations in Two Variables
greatest common factor7.1 Greatest Common Factor and Factor by Grouping, 7.1 Greatest Common Factor and Factor by Grouping
grouping symbols1.2 Use the Language of Algebra
H
horizontal line4.2 Graph Linear Equations in Two Variables
I
identity2.4 Use a General Strategy to Solve Linear Equations, 2.4 Use a General Strategy to Solve Linear Equations
Identity Property of Addition1.9 Properties of Real Numbers
Identity Property of Multiplication1.9 Properties of Real Numbers
improper fractions1.8 The Real Numbers
inconsistent system5.1 Solve Systems of Equations by Graphing
independent5.1 Solve Systems of Equations by Graphing
independent equations5.1 Solve Systems of Equations by Graphing
index9.7 Higher Roots
integers1.3 Add and Subtract Integers, 1.4 Multiply and Divide Integers, 1.8 The Real Numbers
intercepts of a line4.3 Graph with Intercepts
interest3.2 Solve Percent Applications
interval notation2.7 Solve Linear Inequalities
Inverse Property of Addition1.9 Properties of Real Numbers
Inverse Property of Multiplication1.9 Properties of Real Numbers
irrational1.8 The Real Numbers
irrational number1.8 The Real Numbers
L
least common denominator1.6 Add and Subtract Fractions
least common multiple1.1 Introduction to Whole Numbers, 1.1 Introduction to Whole Numbers
like radicals9.3 Add and Subtract Square Roots, 9.7 Higher Roots, 9.7 Higher Roots
like square roots9.3 Add and Subtract Square Roots, 9.4 Multiply Square Roots
like terms1.2 Use the Language of Algebra
linear equation4.1 Use the Rectangular Coordinate System, 4.1 Use the Rectangular Coordinate System
linear inequality4.7 Graphs of Linear Inequalities, 4.7 Graphs of Linear Inequalities
list price3.2 Solve Percent Applications
M
mark-up3.2 Solve Percent Applications
metric system1.10 Systems of Measurement
mixture problems3.3 Solve Mixture Applications
monomial6.1 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
multiples1.1 Introduction to Whole Numbers
multiplication1.2 Use the Language of Algebra, 1.4 Multiply and Divide Integers, 1.4 Multiply and Divide Integers
Multiplication Property of Equality2.2 Solve Equations using the Division and Multiplication Properties of Equality
multiplicative identity1.9 Properties of Real Numbers
multiplicative inverse1.9 Properties of Real Numbers
multiplying fractions1.5 Visualize Fractions
N
negative exponent6.7 Integer Exponents and Scientific Notation, 6.7 Integer Exponents and Scientific Notation
negative numbers1.3 Add and Subtract Integers
negative slope4.4 Understand Slope of a Line
neutral pairs1.3 Add and Subtract Integers
nth root of a number9.7 Higher Roots
number line1.1 Introduction to Whole Numbers, 1.3 Add and Subtract Integers, 1.8 The Real Numbers
number system1.1 Introduction to Whole Numbers
numerator1.5 Visualize Fractions
O
operations1.2 Use the Language of Algebra
opposite1.3 Add and Subtract Integers
Order of Operations1.2 Use the Language of Algebra
ordered pair4.1 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
origin4.1 Use the Rectangular Coordinate System, 4.1 Use the Rectangular Coordinate System
original cost3.2 Solve Percent Applications
P
parabola10.5 Graphing Quadratic Equations, 10.5 Graphing Quadratic Equations
parallel lines4.5 Use the Slope–Intercept Form of an Equation of a Line
percent1.7 Decimals, 3.2 Solve Percent Applications
percent decrease3.2 Solve Percent Applications
percent increase3.2 Solve Percent Applications
perfect square trinomials pattern7.4 Factor Special Products
perimeter3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem, 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
perpendicular4.5 Use the Slope–Intercept Form of an Equation of a Line
perpendicular lines4.5 Use the Slope–Intercept Form of an Equation of a Line
place values1.1 Introduction to Whole Numbers, 1.7 Decimals, 1.7 Decimals
point–slope form4.6 Find the Equation of a Line
point–slope method4.4 Understand Slope of a Line
polynomial6.1 Add and Subtract Polynomials, 6.1 Add and Subtract Polynomials
positive slope4.4 Understand Slope of a Line
prime factorization1.1 Introduction to Whole Numbers, 1.1 Introduction to Whole Numbers
prime number1.1 Introduction to Whole Numbers, 1.1 Introduction to Whole Numbers, 1.5 Visualize Fractions
principal3.2 Solve Percent Applications
principal nth root9.7 Higher Roots
principal square root1.8 The Real Numbers, 9.7 Higher Roots
product1.1 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
profit3.6 Solve Applications with Linear Inequalities
proper fractions1.7 Decimals, 1.8 The Real Numbers
proportion8.7 Solve Proportion and Similar Figure Applications, 8.7 Solve Proportion and Similar Figure Applications
Pythagorean Theorem3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
Q
quadrant4.1 Use the Rectangular Coordinate System
quadratic equation10.1 Solve Quadratic Equations Using the Square Root Property
quadratic equation in two variables10.5 Graphing Quadratic Equations, 10.5 Graphing Quadratic Equations
quadratic equations7.6 Quadratic Equations
quotient1.4 Multiply and Divide Integers, 1.5 Visualize Fractions
R
radical equation9.6 Solve Equations with Square Roots, 9.6 Solve Equations with Square Roots
radical sign1.8 The Real Numbers
rate of interest3.2 Solve Percent Applications
ratio1.5 Visualize Fractions
rational equation8.6 Solve Rational Equations, 8.6 Solve Rational Equations
rational exponents9.8 Rational Exponents, 9.8 Rational Exponents
rational expression8.1 Simplify Rational Expressions, 8.1 Simplify Rational Expressions
rational number1.8 The Real Numbers
rationalize10.1 Solve Quadratic Equations Using the Square Root Property
rationalizing the denominator9.5 Divide Square Roots
real number1.8 The Real Numbers
reciprocal1.5 Visualize Fractions, 1.9 Properties of Real Numbers
rectangle3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
rectangular coordinate system4.1 Use the Rectangular Coordinate System, 4.1 Use the Rectangular Coordinate System
repeating decimal1.7 Decimals
right triangle3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
rise4.4 Understand Slope of a Line, 4.4 Understand Slope of a Line
rounding1.1 Introduction to Whole Numbers
run4.4 Understand Slope of a Line, 4.4 Understand Slope of a Line
S
scientific notation6.7 Integer Exponents and Scientific Notation, 6.7 Integer Exponents and Scientific Notation
similar figures8.7 Solve Proportion and Similar Figure Applications, 8.7 Solve Proportion and Similar Figure Applications
simple interest3.2 Solve Percent Applications, 3.3 Solve Mixture Applications
simplification2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
simplified1.5 Visualize Fractions
simplify an expression1.2 Use the Language of Algebra
slope formula4.4 Understand Slope of a Line, 4.4 Understand Slope of a Line
slope of a line4.4 Understand Slope of a Line
slope–intercept form4.5 Use the Slope–Intercept Form of an Equation of a Line
solution of a linear inequality4.7 Graphs of Linear Inequalities
solution of an equation2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
solutions to a system of equations5.1 Solve Systems of Equations by Graphing
square1.8 The Real Numbers
square root1.8 The Real Numbers
Square Root Property10.1 Solve Quadratic Equations Using the Square Root Property, 10.1 Solve Quadratic Equations Using the Square Root Property
standard form6.1 Add and Subtract Polynomials
subtraction1.2 Use the Language of Algebra
subtraction property1.3 Add and Subtract Integers
Subtraction Property of Equality2.1 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 pattern7.4 Factor Special Products
supplementary angles5.4 Solve Applications with Systems of Equations
system of linear inequalities5.6 Graphing Systems of Linear Inequalities
systems of linear equations5.1 Solve Systems of Equations by Graphing
T
term1.2 Use the Language of Algebra
trinomial6.1 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. system1.10 Systems of Measurement
V
variable1.2 Use the Language of Algebra, 1.2 Use the Language of Algebra, 1.3 Add and Subtract Integers
variables2.3 Solve Equations with Variables and Constants on Both Sides
vertex10.5 Graphing Quadratic Equations, 10.5 Graphing Quadratic Equations
vertical line4.2 Graph Linear Equations in Two Variables
vertices3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
W
whole number1.1 Introduction to Whole Numbers
whole numbers1.8 The Real Numbers
X
x- intercept4.3 Graph with Intercepts
x- intercept of a line4.3 Graph with Intercepts
x-coordinate4.1 Use the Rectangular Coordinate System, 4.1 Use the Rectangular Coordinate System
x-intercept10.5 Graphing Quadratic Equations
x-intercepts of a parabola10.5 Graphing Quadratic Equations
Y
y- intercept4.3 Graph with Intercepts
y- intercept of a line4.3 Graph with Intercepts
y-coordinate4.1 Use the Rectangular Coordinate System, 4.1 Use the Rectangular Coordinate System
y-intercept10.5 Graphing Quadratic Equations
Z
Zero Product Property7.6 Quadratic Equations, 7.6 Quadratic Equations
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