/*! 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 63 Place in the appropriate space t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 63

Place in the appropriate space to make each a true statement. $$ |-5| \quad-(-5) $$

Short Answer

Expert verified
Place '=' between the expressions: 5 = 5.

Step by step solution

01

Understand Absolute Value

Absolute value represents the distance of a number from zero on the number line. For any number \(x\), \(|x|\) is always non-negative. In our case, \(|-5| = 5\), because the distance from \(-5\) to 0 is 5.
02

Simplify the Negative of a Negative

When you have a negative sign in front of another negative sign, they cancel each other out. So, \(-(-5) = 5\). The two negatives become a positive.
03

Compare Both Sides to Place Operand

We need to decide which operand (such as an operator like '+', '-', '*', '/') fits between \(|-5|\) and \(-(-5)\) to make a true statement. We now know both are equal to 5. Since 5 equals 5, we can place the equal sign \(=\) between the two expressions.

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 Negative Numbers
Negative numbers are numbers less than zero. They are represented with a minus sign (e.g., -1, -2, -3). In math, these numbers express values below zero and are used in various contexts, such as temperatures or elevations below sea level. When dealing with negative numbers, it鈥檚 important to remember:
  • The further left a number is on the number line, the smaller it is. This means -5 is smaller than -3.
  • When subtracting a negative number, you are actually adding the positive version; for example, 5 - (-3) becomes 5 + 3.
  • Multiplying or dividing two negative numbers results in a positive number.
Understanding these rules helps in effectively managing operations involving negative numbers.
Using the Number Line
The number line is a visual representation of numbers laid out in order. Every number has a specific position:
  • Zero is typically at the center.
  • Positive numbers are to the right of zero.
  • Negative numbers are to the left of zero.
This makes the number line a useful tool for understanding concepts, like absolute value.
Absolute value, like in the exercise, represents the distance a number is from zero. Whether the number is negative or positive, this distance is always positive. On the number line, you can see how far -5 is from zero鈥�5 steps away. This visual aid helps students grasp the concept of absolute values more intuitively.
Simplifying Expressions
Simplifying expressions involves reducing them to their simplest form, making mathematical operations easier to perform. There are several strategies:
  • Combine like terms: Group similar numbers or variables.
  • Use the associative, commutative, and distributive properties to rearrange terms.
  • Simplify expressions with negative numbers by carefully applying arithmetic rules.
In our step-by-step solution, simplifying \(-(-5)\) involves the rule that two negatives make a positive. So, \(-(-5) = 5\).
By recognizing patterns and applying consistent methods, simplifying expressions becomes a straightforward task, clearing the way for solving more complex problems.

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 each expression. $$ 3^{4} $$

To make an international telephone call, you need the code for the country you are calling. The codes for Mali Republic, C么te d'Ivoire, and Niger are three consecutive odd integers whose sum is \(675 .\) Find the code for each country.

Evaluate each expression. $$ 4^{3} $$

Solve each inequality. Write each answer using solution set notation. $$ 4(3 x-1) \leq 5(2 x-4) $$

Only male crickets chirp. They chirp at different rates depending on their species and the temperature of their environment. Suppose a certain species is currently chirping at a rate of 90 chirps per minute. At this rate, how many chirps occur in one hour? In one 24 -hour day? In one year?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

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.