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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2:07 minutes

Problem 139

Textbook Question

Simplify each expression. See Example 8.3(k + 2) - 5k + 6 + 3

Verified step by step guidance

Distribute the 3 into the expression (k + 2) to get 3k + 6.

Rewrite the expression as 3k + 6 - 5k + 6 + 3.

Combine like terms: 3k and -5k to get -2k.

Combine the constant terms: 6, 6, and 3 to get 15.

Rewrite the simplified expression as -2k + 15.

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Key Concepts

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

Distributive Property

The Distributive Property states that a(b + c) = ab + ac. This property allows us to multiply a single term by each term within a parenthesis, facilitating the simplification of expressions. In the given expression, applying this property to 3(k + 2) will help in breaking it down into simpler components.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This process simplifies expressions by consolidating similar components, making calculations easier. In the expression, terms like -5k and 3k can be combined to streamline the overall expression.

Order of Operations

The Order of Operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. Following these rules is crucial when simplifying expressions to avoid errors.