Problem 1 Writing an Inequality From a Sentence
What inequality represents the sentence, “5 fewer than a number is at least 12.”?
Plan
How can you translate a sentence into an inequality?
Look for key words, such as “at least” or “greater than.”
5 fewer than a number is at least 12.
“Fewer” indicates subtraction.
“At least” indicates greater than or equal to.
✓ Got It?
- What inequality represents the sentence, “The quotient of a number and 3 is no more than 15.”?
The solutions of an inequality are the numbers that make it true. The properties you use for solving inequalities are similar to the properties you use for solving equations. However, when you multiply or divide each side of an inequality by a negative number, you must reverse the inequality symbol.
Take Note Properties: Properties of Inequalities
Let a, b, c, and d represent real numbers.
| Property | Definition | Example |
|---|---|---|
| Transitive | If
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| Addition | If
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| Subtraction | If
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| Multiplication | If
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| If
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| If
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| Division | If
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Here's Why It Works The steps below show that if
Therefore, you need to reverse the inequality symbol when multiplying each side of the inequality
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