/*! 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 32 Simplify. $$ |7| $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 32

Simplify. $$ |7| $$

Short Answer

Expert verified
7

Step by step solution

01

Understand Absolute Value

Absolute value refers to the distance of a number from 0 on the number line, regardless of direction. It is always non-negative.
02

Identify the Number Inside

In this problem, the number inside the absolute value symbols is 7. You need to consider the distance of 7 from 0.
03

Apply Absolute Value Rules

The absolute value of a positive number is the number itself. So, \(|7| = 7\).

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.

Number Line
The number line is a visual representation of numbers laid out in a straight line. It helps us visualize the position of numbers in relation to each other. At the center of this line is zero, which acts as a reference point.
  • To the right of zero, you'll find positive numbers.
  • To the left of zero, negative numbers reside.
Understanding a number's location on this line is key in concepts like absolute value. When we talk about the absolute value of a number, we are interested in its distance from zero, not its direction.
Since distances can't be negative, the absolute value always results in a positive number or zero. For example, the distance of both +7 and -7 from zero on the number line is 7.
Positive Numbers
Positive numbers are numbers greater than zero on the number line. They are placed to the right of zero and include all whole numbers like 1, 2, 3, and so on. Recognizing positive numbers is essential when dealing with absolute values because:
  • The absolute value of a positive number is simply the number itself.
  • Positive numbers remain unchanged when we consider their absolute value.
For instance, in the exercise, the absolute value of 7鈥攐r \( |7| \)鈥攅quals 7, reinforcing that positive numbers retain their value when seen through the lens of absolute value.
This principle applies to any positive number you encounter.
Simplifying Expressions
Simplifying expressions involves reducing them into a more straightforward or familiar form without changing their value. In the context of absolute values, simplifying means converting expressions inside the absolute value bars into their non-negative equivalents.
This is particularly simple when dealing with positive numbers. Here's how it works:
  • Identify the number within the absolute value bars.
  • If the number is positive, or zero, leave it as is.
For example, when simplifying \( |7| \):
  • Recognize that 7 is already a positive number.
  • Since the number is positive, \( |7| = 7 \) means no further changes are necessary.
Thus, the expression is already in its simplest form, illustrating how absolute value conceptually simplifies expressions to their core non-negative values.

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

Represent each quantity by an integer. The Challenger Deep in the Mariana Trench (the deepest-known part of the Pacific Ocean) is the lowest known point in the Earth's seabed hydrosphere. The bottom is estimated to be 35,814 feet below sea level.

Find the opposite of each integer. $$ 123 $$

Evaluate. $$ -|-x| \text { if } x=10 $$

Graph each integer in the list on the same number line. $$ 0,3,10,11 $$

Represent each quantity by an integer. The lowest elevation in the United States is found at Death Valley, California, at an elevation of 282 feet below sea level.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

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.