Problem 40 Determine each value. $$ |-8... [FREE SOLUTION]

Chapter 10: Problem 40

Determine each value. $$ |-8| $$

Short Answer

Expert verified

The absolute value of -8 is 8.

Step by step solution

Understand Absolute Value

The absolute value of a number is the distance of that number from zero on a number line, regardless of direction. Therefore, it is always non-negative.

Apply Absolute Value Definition

Take the given number, -8, and determine its distance from zero. The number -8 is 8 units away from 0, so its absolute value is 8.

Write the Result

Based on the absolute value definition, we find that $|-8|$ equals 8.

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Key Concepts

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

Distance from Zero

When you think about the absolute value, envision it as a measure of how far a number is from zero. It does not matter whether the number is positive or negative when considering its absolute value; what matters is the distance itself. For example, the number $-8$ on a number line is 8 units away from zero. Therefore, the absolute value of $-8$ is 8. This is because only the distance is considered, not the direction.

The focus is solely on how many steps you need to reach zero.
Both $+8$ and $-8$ have the same absolute value of 8.
Absolute value means ignoring the sign and looking at the value itself.

This idea makes absolute values very useful in various mathematical applications where the size of a number is important but its sign is not.

Non-negative Values

Absolute value is fundamentally linked to the concept of non-negative numbers. This means when you calculate the absolute value, the result will always be zero or positive. This principle assures that you're always dealing with a non-negative distance from zero. No matter whether you're dealing with the positive side, like $+8$, or the negative, like $-8$, the absolute value turns it non-negative. Let's remember:

Absolute values are always zero or greater.
Negative inputs, such as $-8$, become positive outputs, such as 8.
This process helps in calculations where size matters but negativity doesn't.

So, whenever you face a number and are asked to find its absolute value, you're essentially stripping away any negative sign to consider only its magnitude.

Number Line Concept

The number line is a simple yet powerful tool that helps us understand absolute value better. Imagine a straight line with zero in the center, positive numbers spaced evenly to the right, and negative numbers to the left. This visualization helps demonstrate why absolute values are non-negative by showing them as distances. On the number line:

Zero is the starting point, which means the absence of distance.
Numbers on the right are positive, and numbers on the left are negative.
Both directions fit into the idea of measuring how far away they are from zero.

To picture $-8$, you locate it on the number line, count how many steps it is to zero, and see that you need 8 units regardless of direction. This upholds the concept that absolute value represents the distance from zero, showcasing its neutrality and non-negative nature on the number line.

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91影视

Determine each value. $$ |-8| $$

Short Answer

Step by step solution

Understand Absolute Value

Apply Absolute Value Definition

Write the Result

Key Concepts

Distance from Zero

Non-negative Values

Number Line Concept

One App. One Place for Learning.

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