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Chapter 1: Problem 83

Write each statement in words and decide whether it is true or false. $$ 15 \leq 15 $$

Short Answer

Expert verified
15 is less than or equal to 15. True.

Step by step solution

01

Understand the Inequality Symbol

The symbol \( \leq \) means 'less than or equal to'. This means that the quantity on the left side is either less than or exactly equal to the quantity on the right side.
02

Write the Statement in Words

The given inequality \( 15 \leq 15 \) can be written in words as '15 is less than or equal to 15'.
03

Determine the Truth of the Statement

When evaluating the inequality \( 15 \leq 15 \), we see that 15 is indeed equal to 15. Since the inequality includes equality (\( \leq \)), this statement is true.

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Key Concepts

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

Inequality Definition
Inequalities are mathematical expressions that show the relationship between two values. They tell us if one value is less than, greater than, less than or equal to, or greater than or equal to another value. Here are some common inequality symbols:
  • <: less than
  • >: greater than
  • 鈮�: less than or equal to
  • 鈮�: greater than or equal to
Inequality symbols help us compare numbers and expressions. They are essential in various math problems, from basic algebra to advanced calculus. For instance, the symbol 鈮� in the inequality 15 鈮� 15 means that 15 is either less than or exactly equal to 15.
True or False Statements
When dealing with inequalities, one key task is determining whether a statement is true or false. To do this, follow these steps:
  • First, understand and decode the inequality symbol used.
  • Next, translate the mathematical expression into words for clarity.
  • Finally, compare the values and check if the inequality holds.
For example, in the statement 15 鈮� 15, the 鈮� symbol tells us that the left side (15) should be less than or equal to the right side (15). Since 15 is equal to 15, this statement is true. So, evaluating inequalities helps us to check the validity of a relationship between two quantities.
Evaluating Inequalities
Evaluating inequalities involves checking the relationship between the two sides of the inequality. The process involves these steps:
  • Identify the inequality symbol and understand its meaning.
  • Rewrite the inequality in words for better comprehension.
  • Compare the values on both sides of the inequality.
Let's evaluate the example 15 鈮� 15.
Step 1: Understand that 鈮� means 'less than or equal to'.
Step 2: Write it in words: '15 is less than or equal to 15'.
Step 3: Compare the numbers. Since 15 is equal to 15, the statement 15 鈮� 15 is true. Evaluating inequalities can help students master comparisons and understand the concepts of inequality more deeply.

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Most popular questions from this chapter

Perform each indicated operation. $$ 6+(-9-2) $$

Perform each indicated operation. $$ 2+(-4-8) $$

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Decide whether each statement is true or false. \(-6 \leq-(-3)\)

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