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Chapter 1: Problem 72

Find each absolute value. $$|3|$$

Short Answer

Expert verified
The absolute value of 3 is 3.

Step by step solution

01

Understand the Concept of Absolute Values

The absolute value of a number is its distance from 0 on the number line. For any number n, \(|n|\) is always positive or zero. In this case, for \(|3|\), because 3 is a positive number, its absolute value is itself.

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Key Concepts

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

Understanding the Number Line
The number line is a visual tool that helps us understand numbers in a straight line.
It includes all numbers, both positive and negative, arranged in increasing order from left to right.
The center of this line is zero.

  • Numbers to the right of zero are positive.
  • Numbers to the left of zero are negative.
  • Each point on the line represents a unique number.
Understanding how numbers are placed on a number line is crucial, especially when dealing with concepts like absolute value.
It visually shows the distance a number is from zero, which is the core idea behind absolute value.
The Role of Positive Numbers
Positive numbers are essential for everyday calculations and understanding absolute value.
These are numbers greater than zero and are located to the right of zero on the number line.

  • Examples include 1, 2, 3, and so on.
  • They are used to represent quantities, distances, and magnitudes in real life.
  • In calculations, they show gain or increase.
When we look at an absolute value, if the number is positive, it stays the same.
Understanding positive numbers helps clarify why \(|3| = 3\).
The distance is already positive and remains unaffected.
Understanding Distance from Zero
Distance from zero is a measure of how far a number is from the center of the number line.
Absolute value equations like \(|3|\) help capture this concept.

  • The concept applies to both negative and positive numbers.
  • For \(|3|\), the distance is directly the positive value itself, 3.
  • Even if a number is negative, the absolute value gives its distance as a positive value.
Understanding distance from zero helps in solving real-world problems.
It may relate to anything needing a non-directional measure鈥攍ike real-world distances or differences in quantities.
Knowing this concept aids in grasping that absolute values are non-negative, reflecting distances on a number line.

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Most popular questions from this chapter

Simplify each algebraic expression. $$4-6 b-8-3 b$$

Order the expressions \(|x-y|,|x|-|y|,\) and \(|x+y|\) from least to greatest for \(x=-6\) and \(y=-8\).

Simplify each series of additions and subtractions. $$-19-8-(-6)+(-21)$$

Simplify each algebraic expression. $$3 x-9 x$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The difference between 0 and a negative number is always a positive number.
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