/*! 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 55 Place the correct symbol \((<... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 55

Place the correct symbol \((<,>\), or \(=)\) between the two real numbers.\(|-7| \quad|7|\)

Short Answer

Expert verified
|-7| = |7|

Step by step solution

01

Evaluate |-7|

The absolute value, noted by the modulus sign '|', of -7 is 7. This is because the absolute value of a number is its distance from zero and is always a positive number or zero.
02

Evaluate |7|

The absolute value of 7 is also 7. This is because 7 is already a nonnegative number, and the absolute value of a nonnegative number is the number itself.
03

Compare the two values

After evaluating, both |-7| and |7| are equal to 7. Comparing them, we see that they are equal.

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.

Understanding Real Numbers
Real numbers are the set of all rational and irrational numbers. They include numbers like integers, fractions, and decimals. Essentially, any number you can find on the number line is a real number. Real numbers can be either positive, negative, or zero.
Real numbers are useful in many everyday calculations, from simple arithmetic to more complex mathematics, like calculus. When dealing with real numbers, especially in equations, it鈥檚 crucial to comprehend how each number behaves. For example, negative numbers have opposites that lie the same distance from zero but in the opposite direction.
Exploring Modulus or Absolute Value
The modulus or absolute value of a number tells us how far away the number is from zero without considering its direction. It is always nonnegative.
When you see a number inside vertical bars like \(|-7|\), it means you take the absolute value. So, \(|-7|\) becomes 7 because the distance from zero is 7, ignoring the negative sign. Likewise, \(|7|\) is also 7 because it's already positive.
  • Absolute value gives us a clearer idea of size without the direction.
  • It helps in understanding the magnitude of numbers irrespective of their sign.
Comparison of Numbers Using Absolute Value
Comparing numbers is essential in understanding how they relate on the number line. When using absolute values for comparison, you focus on their magnitude rather than sign or direction.
In the exercise, \(|-7|\) and \(|7|\) both evaluate to 7. By comparing their absolute values, you see they are equal.
  • Use <, >, or = to show the relationship between numbers.
  • Equality of absolute values indicates the same distance from zero.
This method is helpful when comparing negative numbers to each other or to positive ones, ensuring you understand size over sign.

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

Factor the sum or difference of cubes.\(8 t^{3}-1\)

Use a calculator to evaluate each expression. Write your answer in scientific notation. (Round to three decimal places.)(a) \(\left(9.3 \times 10^{6}\right)^{3}\left(6.1 \times 10^{-4}\right)\) (b) \(\frac{\left(2.414 \times 10^{4}\right)^{6}}{\left(1.68 \times 10^{5}\right)^{5}}\)

Factor the difference of two squares.\(16 x^{2}-9 y^{2}\)

Write the number in scientific notation.Thickness of a Soap Bubble: \(0.0000001\) meter

Factor out the common factor.\(3 x+6\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Applied 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.