Problem 57 - Elementary and Intermediate Algebra

Question

Classify each inequality as either true or false. $$ -3 \geq-11 $$

Step-by-Step Solution

Answer

The inequality \( -3 \geq -11 \) is true.

Step 1: Understand the inequality symbol

The symbol \(\geq\) means 'greater than or equal to'. We need to determine if the number on the left side is greater than or equal to the number on the right side.

Step 2: Compare the numbers

Compare -3 and -11. A number is greater if it is to the right on the number line. Since -3 is to the right of -11 on the number line, -3 is greater than -11.

Step 3: Conclude the inequality

Since -3 is greater than -11, the inequality -3 \(\geq\) -11 is true.

Key Concepts

comparing numbers

When we talk about comparing numbers, we mean figuring out which number is bigger or smaller.
This is crucial in understanding inequalities.
Let’s look at the numbers -3 and -11 from our exercise.

On a number line, numbers to the right are greater than numbers to the left.
Imagine a line with -11 on the left and -3 on the right.
Since -3 is to the right of -11, -3 is bigger.
This makes comparing the numbers easier.
By seeing their positions, it’s obvious which is greater.

inequality symbols

Inequality symbols are used to show the relationship between different numbers.
There are a few main inequality symbols that you need to know:

• \(< > \) : greater than
• \( <\) : less than
• \(\geq\) : greater than or equal to
• \(\leq\) : less than or equal to

In our exercise, we used \(\backslash\textgreater =\) which means 'greater than or equal to'.
We need to check if the number on the left (-3) is either bigger than or the same as the number on the right (-11).

By understanding these symbols, we can easily solve inequalities.

number line

A number line is a simple visual tool that helps us understand numbers and their relationships.
Imagine drawing a straight line and marking equal intervals for numbers.
Smaller numbers are on the left and larger numbers on the right.
This makes it easy to see that -3 is to the right of -11.

You can also use a number line to easily see additions and subtractions.
For instance, if you move three steps to the right from -6, you will be at -3.
This kind of visual can really aid in understanding inequalities.