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Chapter 1: Problem 20

The absolute value expression \(|-7|\) represents A. the distance from 7 to -7 . B. the distance from 7 to 0 . C. the distance from -7 to 7 . D. the distance from -7 to 0 .

Short Answer

Expert verified
The distance from -7 to 0.

Step by step solution

01

Understand Absolute Value

The absolute value of a number is the distance between that number and 0 on the number line, regardless of the direction. It is always a non-negative value.
02

Apply the Definition

For \(|-7|\), find the distance from -7 to 0 on the number line.
03

Calculate the Distance

The distance from -7 to 0 is 7 units. Hence, \(|-7| = 7\).
04

Identify the Correct Option

The correct answer is the one that describes the distance from -7 to 0, which is option D.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

distance on number line
When we talk about distance on a number line, we are referring to the space between two points. This space is always measured in non-negative units. On a number line, every point is a specific distance away from zero. If we take two points, let鈥檚 say -7 and 0, the distance between them is simply the number of units you count along the line to get from -7 to 0.
For example:
  • From -7 to 0, you count 7 units.
  • From 0 to 7, you count 7 units.
The direction you travel on the number line doesn鈥檛 matter when measuring distance. What matters is the number of units. This concept is crucial when working with absolute values.
non-negative value
Absolute values are always non-negative. This means they are either positive or zero, never negative. The absolute value of a number, represented by two vertical bars around it, like \(|x|\), is the distance of that number from 0 on the number line.
Here are some examples:
  • The absolute value of -7 is 7, \(|-7| = 7\).
  • The absolute value of 3 is 3, \(|3| = 3\).
  • The absolute value of 0 is 0, \(|0| = 0\).
Even when dealing with negative numbers, the distance from 0 is positive. That鈥檚 the heart of the concept 鈥榓bsolute value鈥� 鈥� no matter where a number is on the number line, its absolute value is always a non-negative measure of distance from zero.
identifying correct mathematical options
To solve problems involving absolute values and number lines, you need to correctly identify the mathematical properties involved. This means understanding definitions and applying them properly. For example, if given the absolute value expression \(|-7|\), you should:
  • Know the absolute value definition: distance from zero.
  • Recognize that distances are always non-negative values.
  • Apply this knowledge to identify \(|-7| = 7\) because the distance from -7 to 0 is 7 units.
When presented with multiple-choice options, ensure you choose the one that accurately reflects the true nature of absolute values and number line distances. This process involves methodically ruling out incorrect options and reaffirming the correct one with logical reasoning based on mathematical principles.

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Most popular questions from this chapter

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