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Chapter 3: Problem 392

In the following exercises, simplify. $$ |14-8|-|-2| $$

Short Answer

Expert verified
The simplified result is 4.

Step by step solution

01

Calculate inside absolute value (14 - 8)

First, simplify the expression inside the first set of absolute value bars: 14 - 8 = 6.
02

Simplify the absolute value of the result

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

Calculate inside absolute value |鈭�2|

Now, simplify the expression inside the second set of absolute value bars: |-2| = 2.
04

Subtract the results from Step 2 and Step 3

Finally, subtract the two results obtained: 6 - 2 = 4.

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Key Concepts

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

Simplifying Expressions
Simplifying expressions is one of the core concepts in algebra. Simplifying means making an expression easier to understand or solve. It involves breaking down complex expressions into simpler parts. Let's look at how to apply this to our example:
We start with the expression \(|14-8|-|-2|\). To simplify it:
  • First, resolve any operations inside absolute value bars.
  • Then calculate the absolute value of the inner results.
  • Finally, perform any remaining operations.
Following these steps helps in systematically simplifying the expression without errors.
Prealgebra
Prealgebra involves the fundamental concepts of arithmetic before advancing to algebra. It's essential for understanding higher-level math. Absolute values and basic operations fall under prealgebra.

Absolute Value:
The absolute value of a number is its distance from zero on a number line, regardless of direction. For example:
  • \(|6| = 6\)
  • \(|-2| = 2\)
In our exercise, understanding the absolute value was critical to simplifying the inner expressions.

Basic Operations:
Prealgebra covers addition, subtraction, multiplication, and division. Mastery of these operations is foundational to solving any arithmetic or algebra problem.
Basic Arithmetic Operations
Basic arithmetic operations are addition, subtraction, multiplication, and division. These operations are fundamental in math problems, including simplifying expressions.

Addition and Subtraction:
These are the first operations learned in arithmetic and are crucial for simplifying expressions:
  • Addition combines numbers to get their total (e.g., \(5+3=8\)).
  • Subtraction finds the difference (e.g., \(8-3=5\)).
In our example:
  • We first subtract: \(14-8=6\).
  • We then consider subtraction of absolute value results: \(6-2=4\).
These steps underline how basic arithmetic operations assist in breaking down and simplifying algebraic expressions step-by-step.

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