3-7 Absolute Value Equations and Inequalities
Objective
To solve equations and inequalities involving absolute value
In the Solve It, Serena's distance from Darius decreases and then increases. You can use absolute value to model such changes.
Essential Understanding You can solve absolute value equations and inequalities by first isolating the absolute value expression, if necessary. Then write an equivalent pair of linear equations or inequalities.
Problem 1 Solving an Absolute Value Equation
Think
How many solutions does the equation have?
There are two values on a number line that are 7 units from 0: 7 and
What are the solutions of
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← Substitute 7 and
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| 7 + 2 = 9 ✓ | 7 + 2 = 9 ✓ |
✓ Got It?
- What are the solutions of
Table of Contents
- 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
- 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 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