Use a number line to determine whether each statement is true or false. See Example 6. -6 < -1

Verified step by step guidance

1. Understand the inequality: The statement is \(-6 < -1\), which means we want to check if \(-6\) is less than \(-1\).
2. Recall the number line order: On a number line, numbers increase as you move from left to right. Smaller numbers are to the left, and larger numbers are to the right.
3. Locate \(-6\) and \(-1\) on the number line: \(-6\) is to the left of \(-1\) because \(-6\) is more negative than \(-1\).
4. Compare their positions: Since \(-6\) is to the left of \(-1\), it means \(-6\) is less than \(-1\).
5. Conclude the truth value: Therefore, the statement \(-6 < -1\) is true.

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 left are smaller, and those to the right are larger. Understanding this helps compare values like -6 and -1 by their positions on the line.

Inequality Symbols and Their Meaning

Inequality symbols such as '<' indicate the relative size between two numbers. For example, 'a < b' means 'a' is less than 'b'. Correct interpretation of these symbols is essential to determine the truth of statements involving inequalities.

Negative Numbers and Their Comparison

Negative numbers are less than zero, but among them, a number with a larger absolute value is actually smaller. For instance, -6 is less than -1 because it lies further left on the number line, despite 6 being greater than 1 in absolute terms.