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Chapter 1: Problem 44

Simplify by finding the absolute value. \(|-14|\)

Short Answer

Expert verified
| -14 | = 14

Step by step solution

01

Understanding Absolute Value

The absolute value of a number refers to its distance from zero on the number line, regardless of its direction. It is always a non-negative number.
02

Remove the Negative Sign

Since absolute value measures the distance to zero, it ignores whether the number is positive or negative. Thus, the absolute value of \(-14\) is simply 14.
03

Write the Final Answer

Therefore, \(|-14| = 14\)

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Key Concepts

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

Number Line
A number line is a visual representation of numbers on a straight, horizontal line. It helps us understand numerical relationships and perform operations with numbers easily. To make the concept clear:
  • Positive numbers are placed to the right of zero.
  • Negative numbers are on the left of zero.
Each point on the number line corresponds to a unique number, and each number has a unique position on the line.
When dealing with absolute values, the number line is especially useful. The absolute value of a number is its distance from zero on this line, regardless of whether it's left (negative) or right (positive). For example, both 14 and -14 are 14 units away from zero on the number line.
Non-Negative Number
A non-negative number is any real number that is zero or positive. In other words, it is a number that is not negative. Absolute values are always non-negative.
Here are some important points about non-negative numbers:
  • Zero is considered non-negative.
  • All positive numbers are non-negative.
  • Negative numbers cannot be non-negative.
When we take the absolute value, for example, \(-14\), we disregard the negative sign. This means \(|-14| = 14\), which is a positive, non-negative value.
Distance from Zero
The concept of distance from zero is pivotal in understanding absolute values. Distance from zero simply refers to how far a number is from zero on the number line.
Here are some key points:
  • The further right a number is on the number line, the greater its distance from zero (e.g., 14).
  • Similarly, the further left a number is, the greater its distance from zero in non-negative terms (e.g., -14).
  • Absolute values measure this distance without considering direction.
For instance, \(-14\) is 14 units away from zero. The absolute value ignores the direction and simply gives us the distance: \(|-14| = 14\). This ensures that the absolute value remains non-negative.

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