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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1:35 minutes

Problem 14

Textbook Question

Evaluate each expression. -|7/2|

Verified step by step guidance

Identify the absolute value expression: \(|\frac{7}{2}|\).

Recall that the absolute value of a number is its distance from zero on the number line, which is always non-negative.

Evaluate the absolute value: \(|\frac{7}{2}| = \frac{7}{2}\).

Apply the negative sign outside the absolute value: -\(\frac{7}{2}\).

The expression simplifies to the negative of the absolute value result.

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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, |7/2| equals 7/2, while |-7/2| also equals 7/2, illustrating that both positive and negative values yield the same absolute value.

Evaluating Expressions

Evaluating an expression involves substituting values for variables and performing the necessary arithmetic operations to simplify the expression to a single numerical value. In this case, evaluating -|7/2| requires first finding the absolute value of 7/2, which is 7/2, and then applying the negative sign to arrive at the final result of -7/2.

Negative Sign in Expressions

A negative sign in front of a number or expression indicates that the value is to be taken as its opposite. In the expression -|7/2|, the negative sign modifies the result of the absolute value operation, changing the positive outcome of 7/2 into -7/2. Understanding how to apply negative signs is crucial for accurate evaluation of mathematical expressions.