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Chapter 1: Problem 20

Evaluate. -|6|

Short Answer

Expert verified
The absolute value of 6 is 6.

Step by step solution

01

Evaluate the absolute value of a positive number

Since the number inside the absolute value symbol (| |) is 6, we can find its absolute value simply by writing the number as it is:
02

Write down the result

The absolute value of 6 is 6.

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Key Concepts

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

Evaluating Expressions
Evaluating expressions involves finding the value of a mathematical expression by following specific rules. In the context of absolute values, an absolute value expression looks like \( |x| \), where \( x \) is any real number. The absolute value of a number is essentially its distance from zero on the number line. This means that it is always a non-negative number, regardless of whether the original number is positive or negative.
To evaluate an absolute value expression:
  • Check if the number inside the absolute value sign is positive, negative, or zero.
  • If the number is positive or zero, its absolute value is the number itself.
  • If the number is negative, ignore the negative sign to find the absolute value.
For example, evaluating the expression \( |-6| \) would simply yield 6, because we drop the negative sign. This process is straightforward and can be easily mastered with practice.
Positive Numbers
Positive numbers are numbers greater than zero. They play a fundamental role in evaluating expressions, particularly those involving absolute values. When looking at positive numbers within an absolute value, the operation is quite simple. The absolute value of a positive number is the number itself.
This is because positive numbers are already at a positive distance from zero, so no changes need to be made. Consider the number 6:
  • It is positive, which means its absolute value is the same number, 6.
  • This illustrates why evaluating the absolute value of a positive number is straightforward.
Understanding this principle helps simplify many mathematical processes, especially when dealing with complex expressions.
Step-by-Step Solutions
Providing step-by-step solutions is an excellent way to understand mathematical problems thoroughly. Breaking down the process into smaller, manageable parts allows for clarity and a better grasp of the concepts involved. For example, when evaluating the expression \( -|6| \):
  • Step 1: Determine the absolute value. Here, the absolute value of 6 is 6 since it is positive.
  • Step 2: Apply the negative sign in front. The final result is -6.
By approaching problems with this method:
  • Each step builds upon the previous one, ensuring you don't miss vital parts of the calculation.
  • You can verify your work as you go, reducing chances of error.
These incremental steps help foster confidence and improve problem-solving abilities over time.

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Most popular questions from this chapter

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