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Chapter 1: Problem 84

Write each statement in words and decide whether it is true or false. $$ 21 \leq 21 $$

Short Answer

Expert verified
21 is less than or equal to 21. The statement is true.

Step by step solution

01

- Understanding the Statement

The given inequality is \(21 \leq 21\). The symbol \( \leq \) means 'less than or equal to'.
02

- Writing the Statement in Words

The inequality \(21 \leq 21\) can be written as: '21 is less than or equal to 21'.
03

- Evaluating the Truth of the Statement

Now, evaluate the statement '21 is less than or equal to 21'. Since 21 is equal to 21, the statement is true.

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Key Concepts

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

writing mathematical statements in words
Mathematical statements use symbols to express relationships between numbers. To understand these relationships better, it's helpful to convert them into words. For example, the inequality \(21 \leq 21\) includes the symbol \( \leq \), which means 'less than or equal to'. So, \(21 \leq 21\) can be written in words as '21 is less than or equal to 21'. This step makes it easier for us to interpret and evaluate the statement by comparing the numbers in a familiar language.
evaluating inequalities
Evaluating inequalities involves determining whether a statement about the relationship between numbers is true or false. For the inequality \(21 \leq 21\), we need to check if 21 is less than or equal to 21. Mathematically, 'less than or equal to' means that the first number can be either less than the second number, or they can be equal. Since 21 is equal to 21, this statement is true. Breaking down inequalities in this manner ensures we understand the direction and condition of the comparison.
understanding mathematical symbols
Mathematical symbols are essential for writing concise statements in algebra. The symbol \( \leq \) stands for 'less than or equal to'. This is crucial when dealing with inequalities as it shows two possible relationships. Knowing what each symbol means is key to interpreting and solving equations and inequalities. For example:
  • \( < \) means 'less than'
  • \( > \) means 'greater than'
  • \( \geq \) means 'greater than or equal to'
This understanding helps us transition easily between symbols and words to assess mathematical statements accurately.

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Most popular questions from this chapter

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 3 if the sum of its digits is divisible by \(3,\) and not otherwise. Show that (a) \(4,799,232\) is divisible by 3 and \((b) 2,443,871\) is not divisible by 3

Find each difference. $$ -\frac{5}{6}-\frac{1}{2} $$

Perform each indicated operation. $$ (3-7)+4 $$

Find each difference. $$ -7-(-5) $$

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