Problem 94 Write a true sentence using eith... [FREE SOLUTION]

Chapter 1: Problem 94

Write a true sentence using either $<,>,$ or $=$. $$|-8| \square|8|$$

Short Answer

Expert verified

$|-8| = |8|$

Step by step solution

- Evaluate the Absolute Values

First, find the absolute values of the given numbers. The absolute value of a number is always non-negative.$|-8| = 8$$|8| = 8$

- Compare the Absolute Values

Next, compare the absolute values that were found in Step 1.$8 \square 8$

- Insert the Correct Symbol

Determine the correct relation. Since both values are equal, use the symbol for equality.$8 = 8$

- Write the True Sentence

Finally, write the true sentence using the symbol found in Step 3.$|-8| = |8|$

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Key Concepts

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

Absolute Value

Absolute value is a concept in mathematics that refers to the distance of a number from zero on the number line. This distance is always non-negative, regardless of the direction. For example, the absolute value of -8 can be denoted as $|-8|$, and it equals 8. Similarly, the absolute value of 8 is also 8. When we talk about absolute values, we look at the magnitude without considering whether it's positive or negative.

Key points to remember:

Absolute value is always non-negative
It measures the distance from zero
For any number x, $ |x| = x $ if x is positive or zero, and $|x| = -x$ if x is negative

Inequalities

Inequalities are mathematical expressions used to compare two values and determine if one is greater than, less than, or equal to the other. The common inequality symbols are:

< signifies 'less than'
> signifies 'greater than'
= signifies 'equal to'
鈮� signifies 'less than or equal to'
鈮� signifies 'greater than or equal to'

In the context of this exercise, we need to determine if the absolute value of -8 is less than, greater than, or equal to the absolute value of 8.

Once we evaluate the absolute values (which become 8 and 8), we see that they are equal. So, we use the equal sign (=) to show $|-8| = |8|$.

Comparison of Numbers

Comparison of numbers is a fundamental skill that involves determining the relationship between two numbers. When comparing numbers:

Start by evaluating any expressions involved, such as absolute values
Next, look at the simplified values
Finally, use the correct inequality symbol to represent their relationship

In this exercise, we've compared two absolute values: $|-8| = 8$ and $|8| = 8$. Since both values are 8, we found that they are equal, prompting us to use the equal sign (=). Therefore, our final true sentence is: $|-8| = |8|$. Always ensure you fully simplify and evaluate expressions before comparing them!

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91影视

Write a true sentence using either \(<,>,\) or \(=\). $$|-8| \square|8|$$

Short Answer

Step by step solution

- Evaluate the Absolute Values

- Compare the Absolute Values

- Insert the Correct Symbol

- Write the True Sentence

Key Concepts

Absolute Value

Inequalities

Comparison of Numbers

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