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Chapter 0: Problem 72

Use a number line to determine whether each statement is true or false. $$ 6>-3 $$

Short Answer

Expert verified
The statement '6 > -3' is true.

Step by step solution

01

Understand the Number Line

Visualize a number line where numbers increase from left to right. The leftmost point represents negative infinity, while the rightmost point represents positive infinity.
02

Locate the Numbers on the Number Line

Identify the positions of the numbers 6 and -3 on the number line. The number 6 is positioned to the right of 0, and -3 is positioned to the left of 0.
03

Compare the Positions

On a number line, a number that is to the right of another number is greater. Since 6 is positioned to the right of -3, it is greater than -3.
04

Determine the Truth of the Statement

Conclude that the statement '6 > -3' is true because 6 is indeed greater than -3 on the number line.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Number Line
When dealing with numbers and their relationships, a number line is a helpful tool. A number line is a straight horizontal line with numbers placed at every evenly spaced point. The line typically extends infinitely in both directions. Toward the right of zero, we find positive numbers and toward the left, we find negative numbers. This visual representation helps us easily compare numbers and understand their value. For example, on a number line, the number 6 is to the right of zero, while -3 is to the left of zero.
Compare Numbers
Comparing numbers with a number line is straightforward. We can see which number is bigger or smaller by looking at their positions. The rule is simple: a number that is located further to the right is greater than a number to its left.
Let's consider the numbers 6 and -3 again. If you visualize or draw a number line, you'll place 6 to the right of zero and -3 to the left of zero. Clearly, 6 is to the right of -3, which means 6 is greater than -3.
Greater Than
The 'greater than' symbol (>) is used to compare two numbers, showing that one number is larger than the other. For example, the statement '6 > -3' reads as '6 is greater than -3'.
To determine if this is true using a number line, locate both numbers on the line. Since 6 is positioned to the right of -3, the statement is true.
Understanding the 'greater than' concept using a number line can aid in solving many math problems by providing a clear and visual explanation.

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Most popular questions from this chapter

Simplify each expression. $$ 6|4-5|-24 \div 3 $$

Write each fraction as a decimal. For repeating decimals, write the answer by first using bar notation and then rounding to the nearest thousandth. See Example 11. $$ \frac{1}{6} $$

If \(a\) is a positive number, is \(-\sqrt{a}\) positive, negative, or not a real number?

Simplify each expression. $$ -9(2)^{2}-(-3)(-2) $$

Simplify each expression. $$ \frac{2(-5)+(-3)(-2)}{-8+3^{2}-1} $$
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