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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1:38 minutes

Problem 95

Textbook Question

Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6.3p - 2r

Verified step by step guidance

Substitute the given values into the expression: replace \( p \) with \( -4 \) and \( r \) with \( -10 \).

The expression becomes \( 3(-4) - 2(-10) \).

Calculate \( 3(-4) \) which involves multiplying 3 by -4.

Calculate \( -2(-10) \) which involves multiplying -2 by -10.

Combine the results of the two calculations to simplify the expression.

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Key Concepts

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

Substitution

Substitution is the process of replacing variables in an expression with their corresponding values. In this case, we substitute p, q, and r with -4, 8, and -10, respectively. This allows us to evaluate the expression accurately by simplifying it to a numerical value.

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 common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In evaluating expressions, following this order is crucial to obtaining the correct answer.

Linear Expressions

Linear expressions are algebraic expressions that involve constants and variables raised to the first power. The expression 3p - 2r is linear because it consists of terms that are linear combinations of the variables p and r. Understanding linear expressions is essential for simplifying and evaluating them correctly.