/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 85 Is the absolute value of a numbe... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 85

Is the absolute value of a number always positive? Why or why not?

Short Answer

Expert verified
The absolute value of a number is always non-negative because it represents distance, which cannot be negative.

Step by step solution

01

Understand the Concept of Absolute Value

The absolute value of a number refers to its distance from zero on the number line, regardless of direction. It is always a non-negative number because distance cannot be negative.
02

Consider Different Cases

Consider a positive number, a negative number, and zero. The absolute value of a positive number (a) is |a| = a. The absolute value of a negative number (-b) is |-b| = b. The absolute value of zero is |0| = 0.
03

Conclusion Based on Examples

From the cases considered, we see that the absolute value of any number is either zero or a positive number. Therefore, it is always non-negative.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Positive Number
Positive numbers are those that are greater than zero. They are found to the right of zero on the number line.
Examples include 1, 2, 3, and so on.

When considering the absolute value of a positive number, it's simple: the absolute value is the number itself.
For instance, the absolute value of 5 is 5, which we can write down as \(|5| = 5\).
Remember, positive numbers are always greater than zero by definition. Therefore, their absolute values also remain positive.
Negative Number
Negative numbers are those that are less than zero. You will find them to the left of zero on the number line.
Examples include -1, -2, -3, and so on.

When determining the absolute value of a negative number, you essentially remove the negative sign.
In LaTeX, the absolute value of a negative number -b is written as \(|-b| = b\). For example, the absolute value of -7 is 7.
Despite being less than zero, the distance from zero is still considered a positive value.
Non-Negative Number
Non-negative numbers include all positive numbers and zero.
Simply, they are numbers that are not negative.
Examples include 0, 1, 2, 3, and all other numbers greater than or equal to zero.

Because the concept of absolute value measures the distance from zero, it is always a non-negative number.
This is because distance, by definition, cannot be negative.
Therefore, whether you start with a positive number, a negative number, or zero, the absolute value will always be zero or a positive number.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Evaluate using a calculator. $$ \frac{1}{2}(x+5 / z)^{2}, \text { for } x=141 \text { and } z=0.2 $$

Given that \(0.3 \overline{3}=\frac{1}{3}\) and \(0.6 \overline{6}=\frac{2}{3},\) express each of the following as a ratio of two integers. $$5.5 \overline{5}$$

Simplify using a calculator. Round your answer to the nearest thousandth. $$ \frac{46-(3-8)^{3}}{2\left[35-(18-26)^{2}\right]} $$

Simplify. $$ 8 x-(6 x+7) $$

SYNTHESIS Is it true that for all real numbers \(a, b,\) and \(c\) $$ a|b-c|=a b-a c ? $$ Why or why not?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.