Table of contents
- 0. Review of Algebra4h 16m
- 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 19m
- 10. Combinatorics & Probability1h 45m
0. Review of Algebra
Algebraic Expressions
1:34 minutes
Problem 147
Textbook Question
Textbook QuestionEvaluate each expression for x = -4 and y = 2. 2|y| - 3|x| / |xy|
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|. For example, |3| = 3 and |-3| = 3. Understanding absolute value is crucial for evaluating expressions that involve both positive and negative numbers.
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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. Correctly applying these rules is essential for accurately evaluating complex expressions.
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Substitution
Substitution involves replacing variables in an expression with their corresponding numerical values. In this case, x = -4 and y = 2 must be substituted into the expression before evaluation. This step is fundamental in simplifying expressions and solving equations, allowing for the calculation of specific values based on given inputs.
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