Problem 41 Evaluate each expression. $$|-... [FREE SOLUTION]

91影视

Understanding Elementary Algebra with Geometry

Lewis Hirsch, Arthur Goodman

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 41

Evaluate each expression. $$|-4|$$

Short Answer

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Step by step solution

Understand Absolute Value

The absolute value of a number is the distance of that number from 0 on the number line, regardless of direction. It is always a non-negative value.

Evaluate the Absolute Value

To find $|-4|$, determine the distance of -4 from 0. Since absolute value removes any negative sign, $|-4|$ is equal to 4.

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Key Concepts

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

distance on number line

When we talk about the distance on a number line, we are essentially measuring how far a number is from another point, typically zero. This measurement disregards direction, only focusing on the 'how far' aspect. For instance, the number -4 is four units away from 0 on the number line. Similarly, the number 4 is also four units away from 0, albeit in the opposite direction.

To visualize this, imagine a straight line with 0 at the center. Moving to the left from 0, you encounter -1, -2, -3, and finally -4. Moving to the right from 0, you encounter 1, 2, 3, and then 4. Hence, the distance of -4 from 0 is exactly the same as the distance of 4 from 0, which is four units.

non-negative value

A non-negative value is any number that is either positive or zero. This means it cannot be a negative number. Absolute values are always non-negative since they represent distance, and distance cannot be negative.

For example, if you take the absolute value of -4, you get 4. This is because distance, as a non-negative value, can never be below 0. Thus, while -4 is a negative number, its absolute value, represented as $|-4|$, is a non-negative value, which is 4. This holds true for any number, whether positive or negative.

evaluate expressions

To evaluate expressions effectively, follow a clear process. First, understand what the expression is asking you to do. In the case of absolute values, this means determining the distance of a number from 0.

For $|-4|$, we know to remove the negative sign to find its distance from 0. Thus, $|-4|$ becomes 4.

Here are steps to evaluate absolute value expressions efficiently:

Identify the number inside the absolute value symbols.
Determine the distance of that number from zero on the number line.
Remove any negative signs to ensure the result is non-negative.

By carefully following these steps, you can evaluate any absolute value expression with ease.

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91影视

Evaluate each expression. $$|-4|$$

Short Answer

Step by step solution

Understand Absolute Value

Evaluate the Absolute Value

Key Concepts

distance on number line

non-negative value

evaluate expressions

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