/*! 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 52 True or false: If \(a\) is neg... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 52

True or false: If \(a\) is negative, then \(|a|=-a\)

Short Answer

Expert verified
True: If \(a\) is negative, then \(|a| = -a\).

Step by step solution

01

Understand the Absolute Value Definition

The absolute value of a number, \(|a|\), is its distance from zero on the number line, regardless of direction. Therefore, \(|a|\) is always non-negative.
02

Consider the Case When \(a\) is Negative

According to the definition, if \(a\) is a negative number, we have \(|a| = -a\) because the absolute value function converts the negative value to its positive equivalent.
03

Verify the Statement

If we let \(a\) be a negative number (for example, \(a = -3\)), the statement \(|a| = -a\) holds true. For \(a = -3\), \(|-3| = -(-3) = 3\), verifying our statement.

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.

Negative Numbers
Negative numbers are numbers less than zero. They are represented with a minus sign in front of them, for example, -1, -2, -3, and so on. These numbers indicate values below zero and are commonly used in various real-life scenarios like temperatures below freezing or financial debts. If you place a negative number on a number line, it will always be on the left side of zero.

It's important to understand that when working with absolute values, negative numbers get converted to their positive counterparts. For example, the absolute value of -4 is 4. This is because absolute value measures how far a number is from zero, without considering its direction.
Number Line
A number line is a straight line that has numbers placed at equal intervals along its length. It's used to visually represent numbers, including positive numbers, negative numbers, and zero. The center point is usually marked as zero.

On the right side of zero, you will find positive numbers like 1, 2, 3, etc. On the left side of zero, you will see negative numbers like -1, -2, -3, etc.
  • Zero is considered neutral鈥攏ot positive or negative.
  • Every number on the left is less than zero.
  • Every number on the right is greater than zero.

To understand absolute value, imagine any number's position on the number line. The absolute value is the distance of that number from zero.
Absolute Value Function
The absolute value function measures how far a number is from zero. It is always non-negative because distance cannot be negative. The notation for absolute value is two vertical bars around the number, like \(|a|\).
  • If the number inside the bars is positive or zero, the absolute value is the number itself. For example, \(|5| = 5\) and \(|0| = 0\).
  • If the number inside the bars is negative, the absolute value is the positive equivalent of that number. For example, \(|-7| = 7\).

In the context of our exercise, if \(|a| \) and \(-a\) always turn the negative value into its positive counterpart, confirming that our original statement is true when \(|a| = -a\) for any negative \(|a|\).

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

Decide whether each statement is true or false. \(|13-8| \leq|7-4|\)

To find the average (mean) of a group of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. \(23,18,13,-4,\) and \(-8\)

Solve each problem. Marcial Echenique owes \(\$ 679.00\) on his Visa account. He returns three items costing \(\$ 36.89, \$ 29.40,\) and \(\$ 113.55\) and receives credit for these on the account. Next, he makes purchases of \(\$ 135.78\) and \(\$ 412.88\) and two purchases of \(\$ 20.00\) each. He makes a payment of \(\$ 400 .\) He then incurs a finance charge of \(\$ 24.57 .\) How much does he still owe?

Find each difference. $$ -7-(-5) $$

Perform each indicated operation. $$ -9+[(3-2)-(-4+2)] $$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

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.