Problem 67 - Introductory Algebra for College Students

Question

Determine whether each inequality is true or false. $$0 \geq-6$$

Step-by-Step Solution

Answer

The inequality \(0 \geq -6\) is true

Step 1: Understanding Inequality Symbols

The '\(\geq\)' symbol means 'greater than or equal to'. Therefore, the inequality \(0 \geq -6\) is saying that 0 is greater than or equal to -6.

Step 2: Position of numbers on a number line

On a number line, numbers to the right are greater than numbers to the left. In this case, 0 is to the right of -6.

Step 3: Decide if the inequality is True or False

Since 0 is to the right of -6 on the number line, it means that 0 is greater than -6. Therefore, the inequality \(0 \geq -6\) is true

Key Concepts

Understanding the Number Line

A number line is a visual tool that helps us see the order of numbers. It's a straight horizontal line where numbers increase as you move to the right and decrease as you move to the left.

On the number line, every point corresponds to a real number. This relationship allows us to compare numbers easily. For example, in the inequality \(0 \geq -6\), we place both 0 and -6 on the number line.

• 0 is positioned to the right of -6.
• This shows that 0 is greater than -6.

Understanding this layout helps in quickly determining which number is larger or smaller.

Greater Than or Equal To (\(\geq\))

The symbol \(\geq\) stands for "greater than or equal to." It's a combination of two ideas:

• Greater than (">"), which means the first number is larger than the second.
• Equal to ("="), which shows the numbers are exactly the same.

In the example \(0 \geq -6\):

• We ask if 0 is greater than -6, which it is.
• We'd also be correct if 0 was equal to -6 for this inequality to be true, but it isn’t.

Being familiar with this symbol is crucial for quickly evaluating inequalities.

True or False Questions

True or false questions help evaluate our understanding of mathematical concepts like inequalities. They require us to decide if a statement is correct based on given information.

When tackling the inequality \(0 \geq -6\):

• You analyze the meaning of the inequality symbol.
• Visualize or use the number line to find the positions of 0 and -6.
• Determine the truth, in this case, since 0 is indeed greater than -6, the statement is true.

These types of questions are excellent for practicing logical reasoning and ensuring clarity in understanding inequalities.