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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1:28 minutes

Problem 9

Textbook Question

CONCEPT PREVIEW Evaluate each expression.3a - 2b, for a = -2 and b = -1

Verified step by step guidance

Identify the expression to evaluate: \(3a - 2b\).

Substitute the given values into the expression: replace \(a\) with \(-2\) and \(b\) with \(-1\).

The expression becomes \(3(-2) - 2(-1)\).

Calculate \(3(-2)\) which involves multiplying 3 by -2.

Calculate \(-2(-1)\) which involves multiplying -2 by -1.

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Key Concepts

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

Algebraic Expressions

Algebraic expressions are mathematical phrases that can include numbers, variables, and operators. In the expression 3a - 2b, 'a' and 'b' are variables that can take on different values. Understanding how to substitute values into these expressions is crucial for evaluating them correctly.

Substitution

Substitution is the process of replacing a variable in an expression with a specific value. In this case, substituting a = -2 and b = -1 into the expression 3a - 2b allows us to compute the value of the expression. This step is fundamental in simplifying and solving algebraic expressions.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which calculations are performed in an expression. Commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), following this order ensures that expressions are evaluated correctly and consistently.