Question

What is \(|-42|\), simplified? A. 42 B. \((-42)\) C. -42 D. \(|42|\)

Short answer

A. 42

Step-by-step solution

- Understanding Absolute Value

Absolute value represents the distance of a number from zero on the number line, regardless of the direction. Thus, it is always a non-negative number.

- Applying Absolute Value to -42

To find \(|-42|\), we need to determine the distance of -42 from 0 on the number line, which is 42.

- Confirming the Answer

Given that the absolute value of -42 is 42, the correct answer is A. 42.

Key concepts

number line

The number line is a visual representation of numbers arranged in sequence. It helps us understand the position and value of numbers.
Imagine a horizontal line where each point represents a number.
Zero is in the middle, with positive numbers extending to the right and negative numbers extending to the left.

When we talk about absolute value, we're considering the distance a number is from zero on this line. Don't worry about direction—just distance.
For example, both 42 and -42 are 42 units away from zero. This is why \(|-42|\) simplifies to 42.

non-negative numbers

Non-negative numbers are numbers that are zero or positive.
They do not include any negative values.
Absolute value, by definition, is non-negative because it measures how far a number is from zero without considering direction.

When calculating \( |-42| \), we are looking for the distance without direction.
Hence, the answer must be non-negative, thus making \( |-42| \) simply 42.

mathematical reasoning

Mathematical reasoning is the process of using logical thinking to solve problems.
It involves understanding concepts and applying them to find solutions.
In this exercise, we used mathematical reasoning to determine the absolute value of -42.

Let's break it down further:

• First, we recognize that absolute value measures distance from zero on the number line.
• Next, knowing absolute value is always non-negative, we convert -42 to its positive counterpart.
• Applying these rules, we confirm that \( |-42| = 42 \).

Thus, using mathematical reasoning helped us step by step reach the conclusion that the correct answer is 42.