Problem 14 - Algebra A Combined Function

Question

Determine whether each statement is true or false. See Examples 1 through 6 and 10. $$ 8 \geq 9 $$

Step-by-Step Solution

Answer

False

Step 1: Understand the inequality symbol

The symbol \( \geq \) represents 'greater than or equal to'. This means the number on the left side must be greater than or equal to the number on the right.

Step 2: Compare the numbers

We need to compare 8 and 9. For an inequality \( a \geq b \) to be true, \( a \) must be greater than or equal to \( b \). Here, \( 8 \) is less than \( 9 \).

Step 3: Determine the truth value

Since 8 is not greater than or equal to 9, the statement \( 8 \geq 9 \) is false.

Key Concepts

Greater Than or Equal To

In mathematics, the symbol \( \geq \) plays a vital role in expressing relationships between numbers. This symbol, known as "greater than or equal to," is used to compare two values. When you see \( a \geq b \), it means \( a \) can either be bigger than \( b \) or exactly the same as \( b \). In simpler terms, \( a \) is not less than \( b \).

• If the number on the left is larger than the one on the right, the inequality is satisfied.
• If both numbers are the same, it is still satisfied.
• However, if the left side is smaller, the inequality does not hold true.

Understanding how this symbol works is crucial when comparing values or solving mathematical problems that involve inequality.

True or False Statements

In the world of math, especially when dealing with inequalities, determining whether a statement is true or false is a fundamental skill. True or false statements are declarations that can be tested and confirmed using logic and mathematics. In the case of a comparison like \( 8 \geq 9 \), you can evaluate this by:

• Checking if the number on the left is greater than the one on the right.
• Considering if they are equal, which would also make the statement true.
• If neither condition is met, the statement is false.

In our specific example, \( 8 \) is less than \( 9 \), so the statement \( 8 \geq 9 \) is false. The skill of determining a statement's truth value is important in logical reasoning and problem-solving.

Comparing Numbers

When comparing numbers, the goal is to evaluate the relative size or value of two or more numbers. This can involve a variety of symbols and concepts, including greater than (\( > \)), less than (\( < \)), and of course greater than or equal to (\( \geq \)). Here are some tips to make comparing numbers easier:

• Always start by looking at the digit positions, which gives a quick view of which is larger, especially in multi-digit numbers.
• For single digits, it's quite straightforward since each number is distinct.
• Use a number line if needed, as it visually shows which numbers are larger or smaller.
• Remember to consider equals, especially when using \( \geq \) or \( \leq \) (less than or equal to).

Using these strategies, we can deduce that 8 is less than 9, and therefore, \( 8 \geq 9 \) does not hold true. Comparing numbers is a fundamental aspect of mathematics that supports decision-making and problem-solving.