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Chapter 0: Problem 44

Find each absolute value and simplify if needed. $$ |-19| $$

Short Answer

Expert verified
19

Step by step solution

01

Understand the absolute value

The absolute value of a number is its distance from 0 on the number line, regardless of direction. This means it is always non-negative.
02

Apply the absolute value

Since absolute value measures distance without regard to direction, \(|-19|\) becomes simply 19.

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Key Concepts

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

number line
To understand absolute value, it's crucial to grasp the concept of a number line first. A number line is a straight, horizontal line that helps us visualize numbers. On this line:
  • Zero is placed in the middle.
  • Positive numbers are positioned to the right of zero.
  • Negative numbers are positioned to the left of zero.
One key aspect of a number line is that each point corresponds to a unique number, and the distance between any two points corresponds to the difference between their numerical values. This visualization aids in understanding both positive and negative numbers and their distances from zero.
non-negative
A fundamental attribute of absolute value is that it is always non-negative. Let's understand what non-negative means:
  • 'Non-negative' refers to a number being either positive or zero.
  • This means a non-negative number is never less than zero.
When we take the absolute value of a number, we are concerned only with its magnitude, not its sign. Therefore, whether you have a positive or a negative number, its absolute value is always a non-negative number. For example, the absolute value of -19 is 19 because we disregard the negative sign and consider only the 'distance' part.
distance from zero
One of the simplest ways to conceptualize absolute value is by thinking about the 'distance from zero.' This idea means:
  • Absolute value measures how far a number is from zero, regardless of direction.
  • Negative signs are ignored because distance cannot be negative.
For instance, \(|-19|\) translates to finding the distance from -19 to 0 on a number line. Since we are only interested in the count of units, regardless of the direction, the value becomes 19. Thus, absolute value is a simple and powerful concept that helps in understanding numerical distances without worrying about negative numbers.

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