Use a number line to determine whether each statement is true or false. -3 > -3

Verified step by step guidance

1. Understand the inequality: The statement is \(-3 > -3\), which means "-3 is greater than -3."
2. Recall the meaning of the 'greater than' symbol (>): It means the number on the left is strictly larger than the number on the right.
3. Visualize the number line: On a number line, numbers increase as you move to the right. Both numbers here are the same point at \(-3\).
4. Since both numbers are equal, \(-3\) is not greater than \(-3\); they are exactly equal.
5. Therefore, the statement \(-3 > -3\) is false because a number cannot be greater than itself.

Key Concepts

Number Line and Ordering of Real Numbers

A number line visually represents real numbers in increasing order from left to right. Numbers to the right are greater than those to the left. Understanding this helps compare values, especially negative numbers, by their position on the line.

Inequality Symbols and Their Meaning

Inequality symbols like '>' (greater than) and '<' (less than) express the relative size of two numbers. For example, 'a > b' means 'a' is strictly greater than 'b'. Recognizing that equality is not included in strict inequalities is crucial.

Properties of Negative Numbers

Negative numbers are less than zero and their order is reversed compared to positive numbers; for instance, -2 is greater than -3 because it is closer to zero. This concept is essential when comparing negative values on the number line.