Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:35 minutes

Problem 47

Textbook Question

Determine whether each statement in Exercises 43–50 is true or false. -π ≥ - π

Verified step by step guidance

Identify the two expressions in the inequality: \(-\pi\) and \(-\pi\).

Recognize that both expressions are identical, meaning they represent the same value.

Understand that when two values are equal, the inequality \(\geq\) (greater than or equal to) holds true.

Conclude that the statement \(-\pi \geq -\pi\) is true because both sides of the inequality are equal.

Remember that any number is always equal to itself, which makes the statement true.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Inequality

An inequality is a mathematical statement that compares two expressions, indicating that one is greater than, less than, or equal to the other. In this case, the inequality involves the comparison of two identical values, -π and -π, which helps in understanding the properties of equality and inequality.

Properties of Real Numbers

The properties of real numbers include various rules that govern their behavior, such as the reflexive property, which states that any number is equal to itself. This property is crucial for evaluating the statement -π ≥ -π, as it confirms that any number is always equal to itself, making the statement true.

True or False Statements

In mathematics, statements can be classified as true or false based on logical reasoning and established definitions. Understanding how to evaluate these statements is essential for determining the validity of inequalities, such as recognizing that -π is indeed equal to -π, thus affirming the truth of the statement.