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Chapter 2: Problem 60

Decide whether each statement is true or false. $$ 10 \leq 10 $$

Short Answer

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Step by step solution

01

Identify the inequality

The given statement is an inequality: \[10 \leq 10\]The symbol \(\leq\) means 'less than or equal to'.
02

Compare the values

Compare the values on both sides of the inequality. Here, both sides have the value 10.
03

Determine the relationship

Since 10 is equal to 10, and the inequality symbol \(\leq\) includes equality ('less than or equal to'), the statement is true.

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Key Concepts

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

Inequality Symbols
Understanding inequality symbols is essential in mathematics. In this exercise, we are given the symbol \( \leq \). This symbol means 'less than or equal to'.
There are other common inequality symbols as well:
  • \( < \) stands for 'less than'
  • \( \leq \) stands for 'less than or equal to'
  • \( > \) stands for 'greater than'
  • \( \geq \) stands for 'greater than or equal to'
  • \( eq \) stands for 'not equal to'
Using these symbols, we can compare different values to determine their relationship.

In the given exercise, \( 10 \leq 10 \) means that 10 is either less than or equal to 10. Since it's actually equal, the statement is true.
Comparing Values
Comparing values is a key step in determining the truth of an inequality statement. Here, we need to compare the numbers on either side of the inequality symbol. For our example, the comparison is between two values that are both 10.

When comparing values:
  • First, identify the numbers involved.
  • Second, determine what the inequality symbol is asking. Here, \( \leq \) invites us to check if the first number is less than or equal to the second.
  • Then, assess the relationship between these numbers by either visualizing a number line, or by simple comparison.

In our problem, both values are equal, making it straightforward to see that 10 is indeed equal to 10. Hence, the inequality \( 10 \leq 10 \) holds true.
True or False Statements
Determining whether an inequality statement is true or false is an essential mathematical skill. Here鈥檚 how to decide:
  • Identify the inequality and the values you need to compare.
  • Understand the meaning of the inequality symbol.
  • Compare the values based on the inequality symbol.


If the relationship described by the inequality symbol matches the actual relationship between the values, then the statement is true.
Otherwise, it is false. In our given problem and solution, \( 10 \leq 10 \) checks out as true because 10 is equal to 10.
If the values had not adhered to the relationship implied by the symbol, the statement would have been false.
Practicing these steps helps strengthen your understanding and ability to evaluate such statements accurately.

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