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Chapter 1: Problem 79

In Exercises \(73-84\), evaluate the given expression. $$|6-2|-|2-6|$$

Short Answer

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Step by step solution

01

- Evaluate inside the first absolute value

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02

- Evaluate inside the second absolute value

Calculate inside the absolute value: for second EvaluateEvaluateegange
03

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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 represents the distance of a number from zero on the number line, regardless of direction. This means the absolute value of a number is always non-negative.
For example:
\[ |6| = 6 \] and \[ |-6| = 6 \]
In simpler terms, if you take the absolute value of any number, you always get a positive result. Let's understand this with the given expression: \[ |6-2|-|2-6| \].
Breaking it down, we first need to evaluate the expressions inside the absolute values:
- \[ 6 - 2 = 4 \]
- \[ 2 - 6 = -4 \]
Now, we take the absolute values:
- \[ |4| = 4 \]
- \[ |-4| = 4 \]
Therefore, the original expression becomes: \[ 4 - 4 = 0 \].
Evaluating Expressions
Evaluating expressions involves calculating the value of an algebraic expression by substituting values for variables and performing the operations in the correct order.
For absolute value problems, start by solving the expressions inside the absolute value symbols before dealing with the absolute value itself.
In our example \[ |6-2| - |2-6| \], the steps to evaluate are:
  • Step 1: Compute the value inside the first absolute value: \[ 6-2 = 4 \].
  • Step 2: Compute the value inside the second absolute value: \[ 2-6 = -4 \].
  • Step 3: Apply the absolute value: \[ |4| = 4 \] and \[ |-4| = 4 \].
This makes it clear that solving each part of the expression separately simplifies the process.
Elementary Algebra
Elementary algebra is the foundation of all higher levels of math and involves understanding variables, constants, and the basic operations used to manipulate algebraic expressions.
Key concepts include:
  • Variables: Symbols (like x or y) that represent unknown values.
  • Constants: Fixed values (like numbers) that do not change.
  • Operations: Addition, subtraction, multiplication, and division.
In the expression \[ |6-2| - |2-6| \], the subtraction operations are performed first, followed by taking the absolute values, and finally, the subtraction of the results.
By mastering these principles, students can tackle various algebra problems with confidence.

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Most popular questions from this chapter

Evaluate the given expression. Remember to follow the order of operations. $$32+16 \div 8-6$$

In Exercises \(73-84\), evaluate the given expression. $$|2-6|-(2-6)$$

If possible, list three numbers that are members and three numbers that are not members of the given set. If it is not possible, explain why. \(\\{t | t \text { is a real number but not a rational number }\\}\)

In Exercises \(73-84\), evaluate the given expression. $$7-3 \cdot 5-1$$

Graph the given set on a number line. $$\\{0,3,7\\}$$
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