/*! 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 76 Fill in the blank with \(<,&g... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 76

Fill in the blank with \(<,>,\) or \(=\) $$-(-4) \square-|-4|$$

Short Answer

Expert verified
4 > -4

Step by step solution

01

Understand the expressions on both sides of the blank

On the left side, there is oindent \(-(-4)\). On the right side, there is oindent\(-|鈭�4|\).
02

Simplify the left side

\(-(-4) = 4\), because the negative sign in front of the -4 makes it positive.
03

Simplify the right side

\(-|鈭�4|\). The absolute value of oindent\(-4\) is oindent \(4\), so oindent \(-|鈭�4| = -4\).
04

Compare the two sides

Comparing the two simplified values, \(4\) on the left side and \(鈭�4\) on the right side, we see that \(4 > 鈭�4\).

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.

absolute value
The absolute value of a number is its distance from zero on the number line. It is always non-negative. You can think of it as taking the 'positive' version of a number.
For example:
- The absolute value of 5, denoted as \(|5| \), is 5.
- The absolute value of -5, denoted as \(|-5| \), is also 5.

In our exercise, we encountered \(|鈭�4| \), which equals 4. The absolute value helps in understanding distances and comparisons without considering direction.
negative numbers
Negative numbers are numbers less than zero. They appear on the left side of the number line.
- For example, -3, -7, and -1 are all negative numbers.

A key property of negative numbers is that multiplying or dividing two negatives gives a positive result:
- For instance, \-(-4) = 4\. Here, we flip the negative sign to get a positive number.

In our exercise, the term \(-(-4) \) simplifies to 4, as two negative signs cancel each other out.
inequalities
Inequalities are mathematical expressions showing the relationship between two values. They use symbols like <, >, <=, >=.
- For example, 3 > 2 means 3 is greater than 2.
- 1 < 4 means 1 is less than 4.

When comparing different sides in our exercise, we simplified to see \(4 \) on the left and \(-4 \) on the right, and concluded that \4 > 鈭�4.袄

This comparison shows how inequalities help us understand which numbers are larger or smaller in value.
prealgebra
Prealgebra lays the foundation for all higher-level math. It involves basic arithmetic, understanding numbers, and simple equations. Learning concepts like:

    - Absolute value: distance from zero.
    - Negative numbers: values less than zero.
    - Inequalities: comparing two values.

    For example, in our exercise, we use prealgebra skills to simplify expressions and make comparisons, like simplifying \(-(-4) \) to 4 and \(-|鈭�4| \) to -4, and then comparing them to see \4 > -4.\

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

For Exercises \(2-7,\) simplify. $$-34+(-13)$$

Place the correct symbol \((>,<, \text { or }=)\) between the two numbers. $$-|-10| \square 10$$

Subtract the integers using a calculator. \(104,839-(-24,938)\)

Fill in the blank with \(<\) or \(>\) to make a true statement. $$8 \square 9$$

Multiply the integers. $$-144(-1)$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

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.