/*! 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 22 Simplify each absolute value exp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 22

Simplify each absolute value expression. (a) \(|5|\) (b) \(|20|\) (c) \(|-19|\)

Short Answer

Expert verified
|5| = 5, |20| = 20, |-19| = 19

Step by step solution

01

Understanding Absolute Value

The absolute value of a number is its distance from zero on a number line, regardless of direction. It is always a non-negative value.
02

Simplify \(|5|\)

Since 5 is already a positive number, \(|5| = 5\).
03

Simplify \(|20|\)

Since 20 is already a positive number, \(|20| = 20\).
04

Simplify \(|-19|\)

Since -19 is a negative number, the absolute value changes it to its positive counterpart: \(|-19| = 19\).

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 and Negative Numbers
In mathematics, numbers can be either positive or negative. Positive numbers are greater than zero and are typically written without a sign, like 5 or 20. These numbers lie to the right of zero on a number line. Negative numbers are less than zero and are marked with a minus sign, such as -19. They are located to the left of zero on the number line. Positive numbers represent quantities that are increasing or in gain, while negative numbers indicate quantities that are decreasing or in loss.
Number Line
A number line is a straight, horizontal line that represents numbers as points along its length. It extends infinitely in both directions and includes positive numbers, negative numbers, and zero. The number line is a crucial visual tool in mathematics for understanding number relationships and operations like addition, subtraction, and absolute value. When you look at the number line, each number is positioned according to its value, with zero in the center. Here are some key points:
  • Positive numbers are to the right of zero.
  • Negative numbers are to the left of zero.
  • Numbers increase in value as you move right and decrease as you move left.
By using a number line, you can easily visualize concepts like distance and direction.
Distance from Zero
The distance of a number from zero on the number line is known as the absolute value. This distance is always a non-negative value because distance cannot be negative. For instance, the distance of 5 from zero is 5 units, and the distance of -19 from zero is also 19 units. The absolute value of a number is written with vertical bars around it, such as \(|5|\) or \(|-19|\). This concept is essential because it helps us understand the magnitude of numbers without considering their direction. In summary:
  • The absolute value of a positive number is the number itself, e.g., \(|5| = 5|\)
  • The absolute value of a negative number is its positive counterpart, e.g., \(|-19| = 19|\)
  • Zero's absolute value is zero, e.g., \(|0| = 0|\).
Understanding absolute values simplifies many mathematical procedures and helps in solving problems more efficiently.

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

In the following exercises, solve each equation using the division property of equality and check the solution. $$ 8 p=72 $$

In the following exercises, evaluate. $$ 35-a \text { when } a=-4 $$

In the following exercises, simplify each expression. $$ 11+(-15)+3 $$

In the following exercises, translate each phrase into an algebraic expression and then simplify, if possible. the quotient of 25 and the sum of \(m\) and \(n\)

In the following exercises, evaluate each expression. $$ \begin{array}{l}{n+4 \text { when }} \\ {\text { (a) } n=-1} \\ {\text { (b) } n=-20}\end{array} $$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

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.