Problem 58 Use either $<,>,$ or \(=... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 10: Problem 58

Use either $<,>,$ or $=$ for $\square$ to write a true sentence: $$ |-5| \square|-2| $$

Short Answer

Expert verified

|-5| > |-2|

Step by step solution

Understanding Absolute Values

The absolute value of a number is its distance from 0 on the number line, regardless of direction. For example, the absolute value of -5 is 5, and the absolute value of -2 is 2.

Calculate Absolute Values

Find the absolute values of the given numbers: $-5$ becomes $|-5|=5$ $-2$ becomes $|-2|=2$

Compare the Values

Compare the absolute values: $5 \text{ and } 2$. Since 5 is greater than 2, we use the symbol $>$.

Write the True Sentence

Now write the true sentence using the comparison symbol $>$: $|-5| > |-2|$.

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Key Concepts

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

absolute value

Absolute value represents the distance a number is from zero on the number line, without considering direction. It's always a positive number or zero. For example, the absolute value of -5 is written as $|-5| = 5$, and for -2, it's $|-2| = 2$. You simply disregard the negative sign to find the absolute value. Understanding absolute value is essential, as it helps us compare values based on magnitude, not their position on the number line.

number line

A number line is a visual representation of numbers laid out in a straight line, where each point corresponds to a number. It's a useful tool for understanding the concept of absolute value. On a number line, absolute value translates to distance from zero. When you look at -5 and -2 on the number line, both are to the left of zero, but -5 is farther from zero than -2. By visualizing this, we understand that the absolute value of -5 (which is 5) is greater than the absolute value of -2 (which is 2). The number line helps us see these distances clearly.

inequality symbols

Inequality symbols are used to compare two values. The most common symbols are $<$ for 'less than', $<$ for 'greater than', and $=$ for 'equal to'. When comparing absolute values, you can determine which symbol to use based on their distance from zero on the number line.

In our exercise, we found that $|-5| = 5$ and $|-2| = 2$. Since 5 is greater than 2, the correct inequality symbol is $>$. Therefore, we write $|-5| > |-2|$. By understanding these symbols, we can accurately express the relationship between two numbers.

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91影视

Use either \(<,>,\) or \(=\) for \(\square\) to write a true sentence: $$ |-5| \square|-2| $$

Short Answer

Step by step solution

Understanding Absolute Values

Calculate Absolute Values

Compare the Values

Write the True Sentence

Key Concepts

absolute value

number line

inequality symbols

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