Problem 48 Find the absolute value. $$ ... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 10: Problem 48

Find the absolute value. $$ |-4| $$

Short Answer

Expert verified

The absolute value of $-4$ is 4.

Step by step solution

- Understand the Definition

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

- Identify the Number

The given number is $-4$.

- Apply the Absolute Value Rule

For any real number $a$, the absolute value is defined as $|a| = a$ if $a \geq 0$, and $|a| = -a$ if $a < 0$.

- Evaluate Absolute Value of -4

Since $-4$ is less than zero, we use the rule for negative numbers: $|-4| = -(-4) = 4$.

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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 arranged in a straight line. This concept helps us understand the position of numbers relative to each other.
鈥� The center of the number line is marked by 0.
鈥� Numbers to the right of 0 are positive, while those to the left are negative.
鈥� The absolute value of a number is its distance from 0 on the number line, regardless of its direction.
For instance, the number $-4$ is 4 units away from zero, just like $4$, but in the opposite direction.
Thus, the absolute value of $-4$ is $4$.

non-negative

Understanding non-negative numbers is crucial in mathematics. A non-negative number is any number that is zero or positive. In simpler terms, it means the number is not negative.
鈥� Absolute values are always non-negative because they represent a distance, and you cannot have a negative distance.
鈥� For example, the absolute value of both $-4$ and $4$ is $4$, a non-negative number.
When you evaluate $|-4|$, you get $4$, not $-4$, because absolute values convert any number to its non-negative form.
Hence, absolute values tell us how far a number is from zero, always using a non-negative result.

evaluate

Evaluating the absolute value of a number involves following a simple rule:
鈥� If the number is zero or positive, its absolute value is the number itself.
鈥� If the number is negative, its absolute value is the positive counterpart of the number.
Here鈥檚 how we apply this rule to $-4$:
- We check if $-4$ is less than zero. Since it is, we use the rule for negative numbers.
- According to the rule, the absolute value of $-4$ is $-(-4)$, which simplifies to $4$.
Therefore, when evaluating $|-4|$, we conclude that the absolute value is $4$.
This process helps ensure clarity and consistency when working with absolute values.

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91影视

Find the absolute value. $$ |-4| $$

Short Answer

Step by step solution

- Understand the Definition

- Identify the Number

- Apply the Absolute Value Rule

- Evaluate Absolute Value of -4

Key Concepts

number line

non-negative

evaluate

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