Problem 41
Question
Explain why \(|-4|=4\).
Step-by-Step Solution
Verified Answer
The absolute value indicates distance from zero, so |−4| is 4
1Step 1: Define Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always a non-negative number.
2Step 2: Apply the Definition
For the number -4, its distance from zero on the number line is 4. Hence, |−4| = 4.
Key Concepts
Number LineNon-Negative NumberDistance from Zero
Number Line
A number line is a straight line that visually represents numbers in sequence.
It extends infinitely in both directions with zero positioned at the center.
Positive numbers are placed to the right of zero, and negative numbers are placed to the left.
Each number has a unique position on the number line.
By using a number line, it's easy to visualize and compare the size of different numbers.
When we talk about the position of a number on this line, we're referring to its numerical value.
It extends infinitely in both directions with zero positioned at the center.
Positive numbers are placed to the right of zero, and negative numbers are placed to the left.
Each number has a unique position on the number line.
By using a number line, it's easy to visualize and compare the size of different numbers.
When we talk about the position of a number on this line, we're referring to its numerical value.
Non-Negative Number
A non-negative number is any number that is zero or greater.
This means non-negative numbers include all positive numbers and zero.
Negative numbers do not fall into this category.
Absolute values are always non-negative because they represent a distance, which can't be negative.
For example, the absolute value of both -4 and 4 is 4, which is a non-negative number. This is because distance, regardless of direction, is always a non-negative quantity.
This means non-negative numbers include all positive numbers and zero.
Negative numbers do not fall into this category.
Absolute values are always non-negative because they represent a distance, which can't be negative.
For example, the absolute value of both -4 and 4 is 4, which is a non-negative number. This is because distance, regardless of direction, is always a non-negative quantity.
Distance from Zero
Distance from zero refers to how far a number is from zero on the number line.
This distance is measured in units and is always a non-negative number.
Regardless of whether the original number is positive or negative, its distance from zero is its absolute value.
For instance, the number -4 is 4 units away from zero.
Thus, \(-4\text){absolutevalue}=4\).
This helps explain why the absolute value of -4 is 4.
Since the concept of distance doesn't change direction, it ensures the absolute value is always non-negative.
This distance is measured in units and is always a non-negative number.
Regardless of whether the original number is positive or negative, its distance from zero is its absolute value.
For instance, the number -4 is 4 units away from zero.
Thus, \(-4\text){absolutevalue}=4\).
This helps explain why the absolute value of -4 is 4.
Since the concept of distance doesn't change direction, it ensures the absolute value is always non-negative.
Other exercises in this chapter
Problem 41
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