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Chapter 0: Problem 56

Find each absolute value and simplify if needed. $$ -|12-6| $$

Short Answer

Expert verified
-6

Step by step solution

01

- Calculate the expression inside the absolute value

First, evaluate the expression inside the absolute value bars: 12 - 6 = 6
02

- Apply the absolute value

Next, find the absolute value of the result from Step 1: |6| = 6
03

- Apply the negative sign

Now, we apply the negative sign outside the absolute value: -|6| = -6

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Key Concepts

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

Understanding Absolute Value
Absolute value is a fundamental concept in mathematics, often represented by vertical bars around a number or expression. It refers to the distance of a number from zero on a number line, regardless of direction.
For instance, both \( |6| \) and \( |-6| \) are equal to 6 because they are both 6 units away from zero. Thus, the absolute value of any number is always non-negative.
In the given problem, we first need to evaluate the expression inside the absolute value bars, \( |12 - 6| \), to understand the distance from zero.
This leads us to our next concept: Evaluation of expressions.
Evaluation of Expressions
Evaluation of expressions involves simplifying mathematical statements step by step to arrive at a solution. When evaluating expressions, particularly those in absolute value problems, follow these steps:
  • First, handle the operations inside the absolute value bars before considering the absolute value.
  • For example, in the expression \( |12 - 6| \), evaluate \( 12 - 6 \) first, which equals 6.
After simplifying the expression inside the bars, we can move to applying the absolute value.
In our example, \( |6| \) is simply 6, as discussed in the previous section. With this simplified, we then address the negative sign outside the absolute value in the final steps.
Order of Operations
Order of operations is crucial in correctly solving mathematical expressions, especially those featuring absolute values and expressions. The standard order is remembered using the acronym PEMDAS:
  • P: Parentheses first
  • E: Exponents (ie. powers and square roots, etc.)
  • M and D: Multiplication and Division (left to right)
  • A and S: Addition and Subtraction (left to right)
In our problem:
  • First, evaluate inside the absolute value bars: \(12 - 6\).
  • Then, find the absolute value: \(|6| = 6\).
  • Finally, apply any remaining operations outside the absolute value, such as the negative sign: \(-|6| = -6\).

    • Following these order of operations ensures accuracy in more complex problems involving absolute values and other mathematical expressions.

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    Most popular questions from this chapter

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