Problem 74 Find each absolute value. $$|x... [FREE SOLUTION]

Chapter 1: Problem 74

Find each absolute value. $$|x|, \text { for } x=-8$$

Short Answer

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Step by step solution

Understand Absolute Value

Absolute value of a number is its distance from zero on the number line, without considering which direction from zero the number lies. It is always non-negative.

Identify the Given Number

The given number is $ x = -8 $.

Apply the Absolute Value Definition

To find the absolute value of $ x $, simply take the non-negative value of the number. So, $ |x| = |-8| $.

Calculate the Absolute Value

Since the absolute value of $ -8 $ is 8, we have $ |-8| = 8 $.

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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 placed in a straight, horizontal line. It helps us understand the concept of absolute value and other number properties. Each point in the number line corresponds to a unique real number.

On a number line, zero is located at the center. Positive numbers are placed to the right of zero, and negative numbers are placed to the left. This positioning helps visualize how far a number is from zero.

For example, if we look at the number line, -8 is eight units to the left of zero. When calculating absolute value, the direction from zero does not matter鈥攐nly the distance.

non-negative values

Non-negative values are numbers that are either positive or zero. Absolute values are always non-negative because they represent distance, which cannot be negative.

For example, if you have the number -8, its absolute value is 8. This is because we are interested in how far -8 is from zero, not the direction.

It is important to remember that even if the original number is negative, its absolute value is non-negative. Thus, applying absolute value turns any negative number into a positive one. For positive numbers and zero, the absolute value remains the same.

distance from zero

Distance from zero is a key concept to understanding absolute value. The absolute value of a number tells us how far that number is from zero on the number line.

For instance, consider the example of -8. The absolute value of -8 is 8 because it is 8 units away from zero, regardless of the direction (left or right).

To determine the absolute value of any number, just measure its distance from zero on a number line without worrying about which side of zero the number is on. This distance is always a positive number or zero.

Understanding this concept is helpful for numerous mathematical operations and real-life applications.

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91影视

Find each absolute value. $$|x|, \text { for } x=-8$$

Short Answer

Step by step solution

Understand Absolute Value

Identify the Given Number

Apply the Absolute Value Definition

Calculate the Absolute Value

Key Concepts

number line

non-negative values

distance from zero

One App. One Place for Learning.

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