Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

0. Review of College Algebra

Solving Linear Equations

Trigonometry

0. Review of College Algebra

Solving Linear Equations

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2:28 minutes

Problem 113

Textbook Question

Identify the property illustrated in each statement. Assume all variables represent real numbers. 1 1(5x) ( — ) = 5 ( x • — ) x x

Verified step by step guidance

Step 1: Observe the given expression: \((5x) \left( \frac{1}{x} \right) = 5 \left( x \cdot \frac{1}{x} \right)\).

Step 2: Recognize that the expression involves multiplication and division of the same variable \(x\).

Step 3: Recall the property of multiplicative inverses: \(a \cdot \frac{1}{a} = 1\) for any non-zero real number \(a\).

Step 4: Apply the property to simplify both sides: \((5x) \cdot \frac{1}{x} = 5 \cdot (x \cdot \frac{1}{x})\).

Step 5: Conclude that the property illustrated is the 'Multiplicative Inverse Property', which states that any number multiplied by its reciprocal equals 1.

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Key Concepts

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

Properties of Equality

The properties of equality state that if two expressions are equal, then they can be manipulated in the same way without changing their equality. This includes operations such as addition, subtraction, multiplication, and division. In the given statement, the manipulation of the fractions illustrates how these properties allow us to simplify or rearrange expressions while maintaining their equivalence.

Distributive Property

The distributive property states that a(b + c) = ab + ac, allowing us to distribute a multiplication over addition or subtraction. In the context of the question, it shows how to distribute the multiplication of 5 across the terms in the fraction, which is essential for simplifying expressions involving variables and constants.

Simplifying Fractions

Simplifying fractions involves reducing them to their simplest form by canceling common factors in the numerator and denominator. In the provided statement, recognizing that the variable 'x' can be canceled from both the numerator and denominator is crucial for simplifying the expression, leading to a clearer understanding of the relationship between the variables.