You can collapse a compound and inequality, like
To solve a compound inequality containing or, find all values of the variable that make at least one of the inequalities true.
Problem 6 Solving an Or Inequality
What is the solution of
Think
How does the solution to an or inequality differ from the solution to an and inequality?
The solution to an or inequality includes all of the solutions of each inequality, not just the solutions of both inequalities.
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Subtraction Property of Inequality |
✓ Got It?
- What is the solution of each compound inequality? Graph the solution.
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✓ Lesson Check
Do you know HOW?
Write an inequality that represents each sentence.
- Rachel's hair is at least as long as Julia's.
- The wind speeds of tropical storms are at least 40 mi/h, but less than 74 mi/h.
Solve each inequality. Graph the solution.
Do you UNDERSTAND?
- Reasoning Make up an example to help explain why you must reverse the inequality symbol when you multiply or divide by a negative number.
- Compare and Contrast Describe how the properties of inequality are similar to the properties of equality and how they differ.
- Write an inequality for which the solution is the set of all real numbers.
- Error Analysis Your classmate says that you cannot write a compound inequality that has no solution. Do you agree? If so, explain why. If not, give a counterexample.
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions