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Elementary Algebra

Key Terms

Elementary AlgebraKey Terms
  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
boundary line
The line with equation Ax+By=CAx+By=C that separates the region where Ax+By>CAx+By>C from the region where Ax+By<CAx+By<C.
geoboard
A geoboard is a board with a grid of pegs on it.
graph of a linear equation
The graph of a linear equation Ax+By=CAx+By=C is a straight line. Every point on the line is a solution of the equation. Every solution of this equation is a point on this line.
horizontal line
A horizontal line is the graph of an equation of the form y=by=b. The line passes through the y-axis at (0,b)(0,b).
intercepts of a line
The points where a line crosses the x- axis and the y- axis are called the intercepts of the line.
linear equation
A linear equation is of the form Ax+By=CAx+By=C, where A and B are not both zero, is called a linear equation in two variables.
linear inequality
An inequality that can be written in one of the following forms:
Ax+By>CAx+ByCAx+By<CAx+ByCAx+By>CAx+ByCAx+By<CAx+ByC

where AandBAandB are not both zero.
negative slope
A negative slope of a line goes down as you read from left to right.
ordered pair
An ordered pair (x,y)(x,y) gives the coordinates of a point in a rectangular coordinate system.
origin
The point (0,0)(0,0) is called the origin. It is the point where the x-axis and y-axis intersect.
parallel lines
Lines in the same plane that do not intersect.
perpendicular lines
Lines in the same plane that form a right angle.
point–slope form
The point–slope form of an equation of a line with slope mm and containing the point (x1,y1)(x1,y1) is yy1=m(xx1)yy1=m(xx1).
positive slope
A positive slope of a line goes up as you read from left to right.
quadrant
The x-axis and the y-axis divide a plane into four regions, called quadrants.
rectangular coordinate system
A grid system is used in algebra to show a relationship between two variables; also called the xy-plane or the ‘coordinate plane’.
rise
The rise of a line is its vertical change.
run
The run of a line is its horizontal change.
slope formula
The slope of the line between two points (x1,y1)(x1,y1) and (x2,y2)(x2,y2) is m=y2y1x2x1m=y2y1x2x1.
slope of a line
The slope of a line is m=riserunm=riserun. The rise measures the vertical change and the run measures the horizontal change.
slope-intercept form of an equation of a line
The slope–intercept form of an equation of a line with slope mm and y-intercept, (0,b)(0,b) is, y=mx+by=mx+b.
solution of a linear inequality
An ordered pair (x,y)(x,y) is a solution to a linear inequality the inequality is true when we substitute the values of x and y.
vertical line
A vertical line is the graph of an equation of the form x=ax=a. The line passes through the x-axis at (a,0)(a,0).
x- intercept
The point (a,0)(a,0) where the line crosses the x- axis; the x- intercept occurs when yy is zero.
x-coordinate
The first number in an ordered pair (x,y)(x,y).
y-coordinate
The second number in an ordered pair (x,y)(x,y).
y-intercept
The point (0,b)(0,b) where the line crosses the y- axis; the y- intercept occurs when xx is zero.
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