Problem 123 Simplify. $$ -\operatorname{... [FREE SOLUTION]

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Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 1: Problem 123

Simplify. $$ -\operatorname{abs}(5) $$

Short Answer

Expert verified

The simplified value is -5.

Step by step solution

Understand Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. So, for any number $x$, $|x|$ is always non-negative.

Find the Absolute Value

For the number 5, the absolute value is calculated as $|5| = 5$. This is because 5 is 5 units away from zero on the number line.

Apply the Negative Sign

Now that we have the absolute value of 5, which is 5, we apply the negative sign in front of the absolute value expression. This means we have $-|5| = -5$.

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Key Concepts

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

Understanding the Number Line

The number line is a visual tool that helps us understand the position of numbers. Imagine a straight line where zero is at the center. Positive numbers are located to the right of zero, while negative numbers are to the left.

Every point represents a specific number, and the distance from zero hints at the absolute value.

Positive numbers move right, getting larger.
Negative numbers move left, getting smaller.

This helps to visualize concepts like addition or subtraction as movement along the line.

Negative Numbers and Absolute Values

Negative numbers are those less than zero, found on the left side of the number line. Unlike positive numbers, negative numbers decrease in value as they move left.

Absolute value, represented as $|x|$, refers to any number's distance from zero on the number line. It is always non-negative because distance cannot be negative.

The absolute value of $+3$ is $|3| = 3$.
The absolute value of $-3$ is also $|-3| = 3$ because it's 3 units from zero.

This concept is crucial when dealing with negative contexts because, regardless of direction, the absolute measure is consistent.

Simplification Techniques

Simplification is all about making expressions easier to understand. It involves reducing complex expressions to simpler forms. Our original exercise, \-\operatorname{abs}(5)\, involves simplification by following a logical flow.

Steps for Simplification:

Identify the Absolute Value: Find out how far the number is from zero without considering direction. For 5, $|5| = 5$.
Apply Operations: After finding the absolute value, apply any additional operations present in the expression. Here, it means applying the negative sign. Thus, \-|5| = -5\.

This process helps convert complex expressions into their simplest form, making calculations easier and interpretations clearer.

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91影视

Simplify. $$ -\operatorname{abs}(5) $$

Short Answer

Step by step solution

Understand Absolute Value

Find the Absolute Value

Apply the Negative Sign

Key Concepts

Understanding the Number Line

Negative Numbers and Absolute Values

Simplification Techniques

Steps for Simplification:

One App. One Place for Learning.

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