/*! 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 40 Evaluate each expression. $$|-... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 40

Evaluate each expression. $$|-15|$$

Short Answer

Expert verified
The absolute value of -15 is 15.

Step by step solution

01

Understanding Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, it's always non-negative.
02

Applying Absolute Value

The expression \(|-15|\) represents the absolute value of -15. This means we need to find how far -15 is from zero on the number line.
03

Calculating Absolute Value

The distance from -15 to 0 on the number line is 15 units. Thus, the absolute value of -15 is 15.

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
When we talk about a number line, imagine a straight horizontal line with numbers lined up at equal intervals. The center of this line is zero, and it extends in both directions indefinitely. On this line, positive numbers are to the right of zero, increasing as they move away from zero. Conversely, negative numbers are to the left of zero, and they become smaller as they move further away from zero.
  • A number line helps visualize the concept of absolute value by showing the distance of a number from zero.
  • Absolute value is represented by vertical bars, like this: \(|-15|\).
For instance, on the number line, \(-15\) is located fifteen units to the left of zero, while \(15\) is fifteen units to the right. The absolute value of a number does not care about its direction; it only considers how far the number is from zero on this line.
Distance from Zero
The phrase 'distance from zero' is crucial when understanding absolute value. It simply means how far a number is from the point marked 0 on the number line, independent of which direction it is. Distance, unlike position, does not have a negative value.
  • To find the absolute value of a number, you check its distance from zero.
  • The absolute value is always a non-negative number, as distance cannot be negative.
So, for \(-15\), we consider its distance from zero, which is 15 units, resulting in \(\|{-15}\| = 15\). This can help in solving problems where both positive and negative values occur.
Non-Negative Numbers
A non-negative number is any number that is either positive or zero. Absolute values are always non-negative numbers because they reflect only the 'distance' from zero, without regard to direction or sign. This is an inherent property of the absolute value function.
  • Non-negative simply means that a number is greater than or equal to zero.
  • When dealing with absolute values, even if you start with a negative number, the result is a non-negative number.
For example, \(-15\) has a distance of 15 from zero. Despite \(-15\) being negative, \(|-15| = 15\), which is non-negative. Understanding this concept is pivotal when evaluating expressions involving absolute 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

Find the value of each expression. $$96 \div(6 \times 8) \div 2$$

The melting point of metal mercury is \(-39^{\circ} \mathrm{C}\). The freezing point of alcohol is \(-114^{\circ} \mathrm{C} .\) How much warmer is the melting point of mercury than the freezing point of alcohol? \(\mathbf{A}-153^{\circ} \mathrm{C}\) c \(75^{\circ} \mathrm{C}\) \(B-75^{\circ} \mathrm{C}\) D \(153^{\circ} \mathrm{C}\)

Determine whether a scatter plot of the data for the following might show a positive, negative, or no relationship. Explain your answer. (lesson \(1-7)\) height and arm length?

Give an example of three integers whose product is negative.

Evaluate each expression $$|0|+|-2|$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Decision 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.