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

Algebraic Expressions

College Algebra

0. Review of Algebra

Algebraic Expressions

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0:58 minutes

Problem 146

Textbook Question

Evaluate each expression for x = -4 and y = 2. |-5y + x|

Verified step by step guidance

Substitute the given values into the expression: replace \( y \) with 2 and \( x \) with -4.

The expression becomes \( |-5(2) + (-4)| \).

Calculate \(-5 \times 2\) to simplify the expression.

Add the result of \(-5 \times 2\) to \(-4\).

Take the absolute value of the result from the previous step.

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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|, and is always non-negative. For example, |5| = 5 and |-5| = 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 = -4 and y = 2 into the expression |-5y + x|. This step is essential for simplifying the expression and obtaining a numerical result, allowing us to evaluate the expression accurately.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which calculations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. Applying these rules correctly is vital when evaluating expressions to avoid errors in calculations.