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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1:48 minutes

Problem 13

Textbook Question

Evaluate each expression. -|4/7|

Verified step by step guidance

Understand that the expression involves the absolute value function, which always returns a non-negative value.

Recognize that the absolute value of a fraction, such as \( \left| \frac{4}{7} \right| \), is simply the fraction itself if it is positive, or its positive counterpart if it is negative.

Since \( \frac{4}{7} \) is already positive, \( \left| \frac{4}{7} \right| = \frac{4}{7} \).

The expression given is \(-\left| \frac{4}{7} \right|\), which means you need to take the negative of the absolute value.

Thus, the final step is to apply the negative sign to the absolute value result, resulting in \(-\frac{4}{7}\).

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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, |4| = 4 and |-4| = 4, indicating that both 4 and -4 are 4 units away from zero.

Rational Numbers

Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. They include integers, fractions, and finite or repeating decimals. The expression -4/7 is a rational number because it can be written as a fraction with -4 as the numerator and 7 as the denominator.

Evaluating Expressions

Evaluating an expression involves substituting values for variables and performing the necessary arithmetic operations to simplify it. In this case, evaluating -|4/7| requires first finding the absolute value of 4/7, which is 4/7, and then applying the negative sign, resulting in -4/7.