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Chapter 1: Problem 94

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

Short Answer

Expert verified
\(|-8| = |8|\)

Step by step solution

01

- Evaluate the Absolute Values

First, find the absolute values of the given numbers. The absolute value of a number is always non-negative.\(|-8| = 8\)\(|8| = 8\)
02

- Compare the Absolute Values

Next, compare the absolute values that were found in Step 1.\(8 \square 8\)
03

- Insert the Correct Symbol

Determine the correct relation. Since both values are equal, use the symbol for equality.\(8 = 8\)
04

- 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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Most popular questions from this chapter

To find the difference between a and b, we subtract b from a. Subtract 19 from \(-7\)

Find the reciprocal of each number, if it exists. $$ \frac{43}{-24} $$

Fill in the blank using one of the following terms: natural number, whole number, integer, rational number, terminating, repeating, irrational number, absolute value. 0 is the only _______ that is not a natural number.

In each of Exercises \(1-8\) fill in the blank using one of the following terms: natural number, whole number, integer, rational number, tern ting irrational. Any number of the form \(a / b,\) where \(a\) and \(b\) are integers, with \(b \neq 0,\) is an example of a(n)__________.

Graph each rational number on the number line. $$ 3.87 $$
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