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Chapter 1: Problem 39

Evaluate each expression. $$|4|$$

Short Answer

Expert verified
4

Step by step solution

01

Identify the Absolute Value Symbol

Notice the vertical bars around the number 4. These bars represent the absolute value of the number.
02

Understand the Definition of Absolute Value

The absolute value of a number is the distance of that number from 0 on the number line, without considering direction. In other words, it's always a non-negative number.
03

Evaluate the Absolute Value

Since 4 is already a positive number, its absolute value is simply 4. Thus, \(|4| = 4\).

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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 in a straight line. It is an essential tool for understanding many mathematical concepts, including absolute value.
A number line typically has marks or points equidistant from each other, representing numbers in sequence.

To the right of zero are positive numbers, while to the left are negative numbers. Zero is usually the central point.
Number lines help us see the relative positions of numbers and their distances from zero.
distance
In the context of a number line, distance refers to how far apart two points are from each other.
When computing absolute values, we measure the distance of a number from zero.

For example, the distance of the number 4 from zero is simply the length of four units to the right. It doesn't matter if we move right or left; what we care about is the non-negative value.
This is why the absolute value of -4 is also 4, as it is four units to the left of zero.
Absolute value always measures this distance, never the direction.
non-negative numbers
Non-negative numbers include zero and all positive numbers.
They do not include any negative numbers.
When we mention non-negative numbers, we refer to values either equal to or greater than zero.

Absolute values are always non-negative. This is because they represent the distance of a number from zero.
For instance, \(|4| = 4\)
Here, 4 is already non-negative, so its absolute value is just 4.
Similarly, \(|-4| = 4\)
This is because we only care about the distance from zero, not the direction.

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Most popular questions from this chapter

Evaluate the given expression. Remember to follow the order of operations. $$(30-5)(4-2)$$

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In Exercises \(73-84\), evaluate the given expression. $$9-(5 \cdot 4-2)$$

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Compute the given expression. Round off your answer to two decimal places where necessary. $$\frac{-12}{-1.2}-\frac{-10}{2.5}$$
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