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Chapter 3: Problem 374

In the following exercises, simplify. $$ |-42| $$

Short Answer

Expert verified
42

Step by step solution

01

Understand Absolute Value

The absolute value of a number is the distance between the number and zero on a number line, regardless of direction. It is always non-negative.
02

Apply Absolute Value

Given the number \(-42\), apply the absolute value concept. The absolute value of \(-42\) is the distance from \(-42\) to 0, which is 42.
03

Simplified Result

Therefore, the absolute value of \(-42\) is \(|-42| = 42\).

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Key Concepts

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

absolute value explanation
Absolute value is a very important concept in math that helps us measure how far a number is from zero, no matter what direction it is in.

Think of it as the number's distance from zero on a number line.

For example, the absolute value of \(-42\) is written as \(|-42|\). It does not matter that \(-42\) is negative, because we are only interested in how far it is from zero. The distance from \(-42\) to 0 is 42, so the absolute value of \(-42\) is 42.
simplifying expressions
Simplifying expressions can sometimes feel challenging.

But viewing each step clearly can make it manageable.

In our problem, we need to simplify \(|-42|\).

First, understand what the absolute value represents. Then apply the definition to the given number: it shows how far \(-42\) is from zero without considering the negative sign. The calculation only involves counting the distance from negative 42 to zero on the number line, which is 42.

So, the simplified form of \(|-42|\) is simply 42.
number line distance
A number line is a great tool to visualize absolute value.

It helps you understand distances between numbers and zero.

Imagine a line with zero in the middle. Negative numbers are on the left, and positive numbers are on the right.

In our problem, we start from \(-42\) and measure the distance to zero.

Count each step until you reach zero. You will find that you need to move 42 steps to the right to reach zero.

Hence, \(|-42|\), the distance between \(-42\) and zero on the number line, is 42.

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