Table of contents

0. Review of Algebra4h 18m
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 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:49 minutes

Problem 63

Textbook Question

In Exercises 61–66, evaluate each algebraic expression for x=2 and y=-5. |x|+|y|

Verified step by step guidance

Identify the given values: \( x = 2 \) and \( y = -5 \).

Understand that the expression involves absolute values: \(|x| + |y|\).

Calculate the absolute value of \( x \): \(|x| = |2| = 2\).

Calculate the absolute value of \( y \): \(|y| = |-5| = 5\).

Add the absolute values together: \(|x| + |y| = 2 + 5\).

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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, |2| equals 2, and |-5| equals 5. Understanding absolute value is crucial for evaluating expressions that involve both positive and negative numbers.

Substitution

Substitution is the process of replacing a variable in an expression with a specific value. In this case, we substitute x with 2 and y with -5 in the expression |x| + |y|. This technique is fundamental in algebra as it allows us to evaluate expressions and solve equations by simplifying them with known values.

Evaluating Expressions

Evaluating an expression involves calculating its value by performing the operations indicated, using the substituted values for any variables. In the expression |x| + |y|, after substituting x and y, we compute the absolute values and then add them together. This concept is essential for finding numerical results from algebraic expressions.