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6-5 Linear Inequalities
Objectives To graph linear inequalities in two variables
To use linear inequalities when modeling real-world situations
Lesson Vocabulary
- linear inequality
- solution of an inequality
A linear inequality in two variables, such as
Essential Understanding A linear inequality in two variables has an infinite number of solutions. These solutions can be represented in the coordinate plane as the set of all points on one side of a boundary line.
Problem 1 Identifying Solutions of a Linear Inequality
Is the ordered pair a solution of
Think
Have you tested solutions before?
Yes. You have tested whether ordered pairs are solutions of equations. Now you will test ordered pairs to see whether they satisfy an inequality.
| A (1, 2) |
B (
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|---|---|---|
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← Write the inequality. → |
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← Substitute. → |
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← Simplify. → |
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| (1, 2) is a solution. | (
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Got It?
- Is (3, 6) a solution of
-
Reasoning Suppose an ordered pair is not a solution of
Table of Contents
Prentice Hall Algebra 1
Selected Answers
Index
Acknowledgments
Contents in Brief
Series Authors
Consulting Authors
Program Authors
Reviewers National
From the Authors
Power Algebra.com
Big Ideas
Exploring Concepts
Thinking Mathematically
Active Learning
Practice Makes Perfect
Pearson Video Challenge
Acing the Test
Entry-Level Assessment
Chapter 1 Foundations for Algebra
Chapter 1 Get Ready!
1-1 Variables and Expressions
1-2 Order of Operations and Evaluating Expressions
1-3 Real Numbers and the Number Line
1-4 Properties of Real Numbers
1 Mid-Chapter Quiz
1-5 Adding and Subtracting Real Numbers
1-6 Multiplying and Dividing Real Numbers
1-7 The Distributive Property
1-8 An Introduction to Equations
1-9 Patterns, Equations, and Graphs
1 Pull It All Together
1 Chapter Review
1 Chapter Test
1 Cumulative Test Prep
Chapter 2 Solving Equations
Chapter 2 Get Ready!
2-1 Solving One-Step Equations
2-2 Solving Two-Step Equations
2-3 Solving Multi-Step Equations
2-4 Solving Equations With Variables on Both Sides
2-5 Literal Equations and Formulas
2 Mid-Chapter Quiz
2-6 Ratios, Rates, and Conversions
2-7 Solving Proportions
2-8 Proportions and Similar Figures
2-9 Percents
2-10 Change Expressed as a Percent
2 Pull It All Together
2 Chapter Review
2 Chapter Test
2 Cumulative Test Prep
Chapter 3 Solving Inequalities
- 2-1 and 2-2 Solving One- and Two-Step Equations
- 2-3 Solving Multi-Step Equations
- 2-4 Solving Equations With Variables on Both Sides
- 2-5 Literal Equations and Formulas
- 2-6 Ratios, Rates, and Conversions
- 2-7 and 2-8 Solving Proportions and Using Similar Figures
- 2-9 Percents
- 2-10 Change Expressed as a Percent
Chapter 3 Get Ready!
3-1 Inequalities and Their Graphs
3-2 Solving Inequalities Using Addition or Subtraction
3-3 Solving Inequalities Using Multiplication or Division
3-4 Solving Multi-Step Inequalities
3 Mid-Chapter Quiz
3-5 Working With Sets
3-6 Compound Inequalities
3-7 Absolute Value Equations and Inequalities
3-8 Unions and Intersections of Sets
3 Pull It All Together
3 Chapter Review
3 Chapter Test
3 Cumulative Test Prep
Chapter 4 An Introduction to Functions
- 3-1 Inequalities and Their Graphs
- 3-2 Solving Inequalities Using Addition or Subtraction
- 3-3 Solving Inequalities Using Multiplication or Division
- 3-4 Solving Multi-Step Inequalities
- 3-5 Working With Sets
- 3-6 Compound Inequalities
- 3-7 Absolute Value Equations and Inequalities
- 3-8 Unions and Intersections of Sets
Chapter 4 Get Ready!
4-1 Using Graphs to Relate Two Quantities
4-2 Patterns and Linear Functions
4-3 Patterns and Nonlinear Functions
4 Mid-Chapter Quiz
4-4 Graphing a Function Rule
4-5 Writing a Function Rule
4-6 Formalizing Relations and Functions
4-7 Sequences and Functions
4 Pull It All Together
4 Chapter Review
4 Chapter Test
4 Cumulative Test Prep
Chapter 5 Linear Functions
Chapter 5 Get Ready!
5-1 Rate of Change and Slope
5-2 Direct Variation
5-3 Slope-Intercept Form
5-4 Point-Slope Form
5 Mid-Chapter Quiz
5-5 Standard Form
5-6 Parallel and Perpendicular Lines
5-7 Scatter Plots and Trend Lines
5-8 Graphing Absolute Value Functions
5 Pull It All Together
5 Chapter Review
5 Chapter Test
5 Cumulative Test Prep
Chapter 6 Systems of Equations and Inequalities
Chapter 6 Get Ready!
6-1 Solving Systems by Graphing
6-2 Solving Systems Using Substitution
6-3 Solving Systems Using Elimination
6-4 Applications of Linear Systems
6 Mid-Chapter Quiz
6-5 Linear Inequalities
6-6 Systems of Linear Inequalities
6 Pull It All Together
6 Chapter Review
6 Chapter Test
6 Cumulative Test Prep
Chapter 7 Exponents and Exponential Functions
Chapter 7 Get Ready!
7-1 Zero and Negative Exponents
7-2 Scientific Notation
7-3 Multiplying Powers With the Same Base
7-4 More Multiplication Properties of Exponents
7 Mid-Chapter Quiz
7-5 Division Properties of Exponents
7-6 Exponential Functions
7-7 Exponential Growth and Decay
7 Pull It All Together
7 Chapter Review
7 Chapter Test
7 Cumulative Test Prep
Chapter 8 Polynomials and Factoring
Chapter 8 Get Ready!
8-1 Adding and Subtracting Polynomials
8-2 Multiplying and Factoring
8-3 Multiplying Binomials
8-4 Multiplying Special Cases
8 Mid-Chapter Quiz
8-5 Factoring x2 + bx + c
8-6 Factoring ax2 + bx + c
8-7 Factoring Special Cases
8-8 Factoring by Grouping
8 Pull It All Together
8 Chapter Review
8 Chapter Test
8 Cumulative Test Prep
Chapter 9 Quadratic Functions and Equations
Chapter 9 Get Ready!
9-1 Quadratic Graphs and Their Properties
9-2 Quadratic Functions
9-3 Solving Quadratic Equations
9-4 Factoring to Solve Quadratic Equations
9 Mid-Chapter Quiz
9-5 Completing the Square
9-6 The Quadratic Formula and the Discriminant
9-7 Linear, Quadratic, and Exponential Models
9-8 Systems of Linear and Quadratic Equations
9 Pull It All Together
9 Chapter Review
9 Chapter Test
9 Cumulative Test Prep
Chapter 10 Radical Expressions and Equations
Chapter 10 Get Ready!
10-1 The Pythagorean Theorem
10-2 Simplifying Radicals
10-3 Operations With Radical Expressions
10 Mid-Chapter Quiz
10-4 Solving Radical Equations
10-5 Graphing Square Root Functions
10-6 Trigonometric Ratios
10 Pull It All Together
10 Chapter Review
10 Chapter Test
10 Cumulative Test Prep
Chapter 11 Rational Expressions and Functions
Chapter 11 Get Ready!
11-1 Simplifying Rational Expressions
11-2 Multiplying and Dividing Rational Expressions
11-3 Dividing Polynomials
11-4 Adding and Subtracting Rational Expressions
11 Mid-Chapter Quiz
11-5 Solving Rational Equations
11-6 Inverse Variation
11-7 Graphing Rational Functions
11 Pull It All Together
11 Chapter Review
11 Chapter Test
11 Cumulative Test Prep
Chapter 12 Data Analysis and Probability
Chapter 12 Get Ready!
12-1 Organizing Data Using Matrices
12-2 Frequency and Histograms
12-3 Measures of Central Tendency and Dispersion
12-4 Box-and-Whisker Plots
12-5 Samples and Surveys
12 Mid-Chapter Quiz
12-6 Permutations and Combinations
12-7 Theoretical and Experimental Probability
12-8 Probability of Compound Events
12 Pull It All Together
12 Chapter Review
12 Chapter Test
End-of-Course Assessment to Prepare for the Algebra I ADP End-of-Course Exam
Skills Handbook
Prime Numbers and Composite Numbers
Factors and Multiples
Using Estimation
Simplifying Fractions
Fractions and Decimals
Adding and Subtracting Fractions
Multiplying and Dividing Fractions
Fractions, Decimals, and Percents
Exponents
Perimeter, Area, and Volume
Line Plots
Bar Graphs
Line Graphs
Circle Graphs
Stem-and-Leaf Plots
Reference
Table 1 Measures
Table 2 Reading Math Symbols
Properties and Formulas
Formulas of Geometry
Visual Glossary
- Chapter 1 Foundations for Algebra
- Chapter 2 Solving Equations
- Chapter 3 Solving Inequalities
- Chapter 4 An Introduction to Functions
- Chapter 5 Linear Functions
- Chapter 6 Systems of Equations and Inequalities
- Chapter 7 Exponents and Exponential Functions
- Chapter 8 Polynomials and Factoring
- Chapter 9 Quadratic Functions and Equations
- Chapter 10 Radical Expressions and Equations
- Chapter 11 Rational Expressions and Functions
- Chapter 12 Data Analysis and Probability