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Chapter 1: Problem 18

Evaluate. $$ |-23| $$

Short Answer

Expert verified
Based on the step-by-step solution provided, the short answer to evaluate the given expression \(|-23|\) is 23.

Step by step solution

01

Identify the number inside the absolute value function

The number inside the absolute value brackets is -23.
02

Determine the distance of the number from zero on the number line

We want to determine the distance of -23 from zero. The distance is measured as a positive or non-negative value.
03

Evaluate the absolute value

Since the distance of -23 from zero is 23 units, the absolute value of -23 is 23. Therefore, \(|-23|\) = 23.

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Key Concepts

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

Negative Numbers
Negative numbers are numbers that are less than zero. You'll find them easily by looking for the minus sign (-) in front of them. These numbers exist on the left side of the number line. They have many practical applications, like representing debts or temperatures below freezing. The concept of negative numbers is essential because it pairs with positive numbers, creating what we call integers.

Here's how negative numbers work in a few key ways:
  • They come after a zero on the number line, which separates positive and negative numbers.
  • The further left you go, the smaller the number becomes, so -23 is smaller than -10 but larger than -50 on a number line.
  • When dealing with absolute values, like in the problem \(|-23|\), negative numbers switch to their positive counterparts, indicating a distance from zero rather than a value below it.
Number Line
A number line is a visualization tool for understanding numbers, whether they're positive, negative, or zero. Picture it as a horizontal line with zero at the center. To the right of zero, positive numbers grow bigger. To the left, negative numbers become smaller. This visual representation makes it easier to comprehend distances between numbers and understand their relative sizes.

Why is the number line helpful?
  • It helps find distances between numbers, from negative numbers to zero, which is essential for understanding concepts like absolute value.
  • It visually demonstrates how integers, both negative and positive, are ordered and spaced.
  • It aids in solving problems involving addition and subtraction by showing direction on the line, moving left or right.

In today's example exercise, \(|-23|\), using the number line would show how far -23 is from zero, solidifying our understanding of absolute value.
Integer Distance Evaluation
Evaluating integer distances often means finding out how far a number is from zero, typically considering it as positive. In mathematics, this concept is tied to absolute value, as it measures 'distance' regardless of direction.
Here's how we evaluate distances:
  • Identify the integer, in this case, -23, and strip away its sign. \(|-23|\) essentially asks 'how far is -23 from zero?' without considering direction.
  • The absolute value of any integer, whether negative like -23 or positive like 23, is always a non-negative number.
  • In our case, the distance from zero to -23 is 23 units, forming a positive 23. This shows how absolute values turn distances into simple, positive numbers.

Our original exercise was to evaluate \(|-23|\), which interprets the integer distance as 23 units, effectively stripping the negative sign and considering only the magnitude of the distance.

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