Chapter 2: Problem 42
Use \(<\) or \(>\) to write a true statement. $$-2 ?-7$$
Short Answer
Expert verified
-7$$
Answer: The correct inequality symbol to make the statement true is \(>\), resulting in the true statement $$-2 > -7$$.
Step by step solution
01
Analyze the numbers given
In this case, we are given two negative numbers: -2 and -7. When dealing with negative numbers, the number with the smaller absolute value, or the number closer to 0, is considered greater.
02
Determine which number is greater
Since -2 is closer to 0 than -7, it is considered greater in value.
03
Choose the correct inequality symbol
Using this information, we can choose the correct inequality symbol to make the statement true. In this case, the correct symbol is \(>\), because -2 is greater than -7.
04
Write the final true statement
Now that we have the correct inequality symbol, we can write the true statement. The final solution is: $$-2 > -7$$
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Negative Numbers
Negative numbers are numbers that are less than zero. They are usually marked with a minus sign \( - \) in front. Unlike positive numbers, where larger numbers have greater value, the ordering of negative numbers is somewhat reversed. As you move further below zero, the values of negative numbers decrease. For example, \(-7\) is less than \(-2\), because \(-7\) is further away from zero on the number line. Understanding this nature of negative numbers is key to comparing them correctly.
Remember:
Remember:
- Negative numbers are less than zero.
- The more negative a number, the smaller it is.
- The number closer to zero is larger when comparing two negative numbers.
Absolute Value
Absolute value is a concept that tells us how far a number is from zero, regardless of its direction on the number line. The absolute value of a negative number is simply its numerical part, without the negative sign. So, the absolute value of both \( -7 \) and \( 7 \) is \( 7 \).
Understanding absolute value is crucial, especially when comparing negative numbers. By comparing their absolute values, you can easily figure out which number is closer to zero. For example, since the absolute value of \( -2 \) is \( 2 \) and \( -7 \) is \( 7 \), you can see \( -2 \) is closer to zero and thus bigger on a number line than \( -7 \).
Key points about absolute value:
Understanding absolute value is crucial, especially when comparing negative numbers. By comparing their absolute values, you can easily figure out which number is closer to zero. For example, since the absolute value of \( -2 \) is \( 2 \) and \( -7 \) is \( 7 \), you can see \( -2 \) is closer to zero and thus bigger on a number line than \( -7 \).
Key points about absolute value:
- It removes the negative sign from negative numbers.
- It represents a number's distance from zero.
- It helps to easily judge which negative number is greater.
Number Comparison
Comparing numbers is a fundamental mathematical concept that helps in understanding their order, be it positive or negative. The first thing to consider when comparing numbers is their magnitude and position on the number line.
When dealing with negative numbers, remember:
When dealing with negative numbers, remember:
- The greater the number closer to zero, the larger it is.
- Always compare the absolute values to see which number has a smaller distance from zero.
- Consider negative numbers in reverse order: \(-7\) is less than \(-2\) because it is further from zero.
Inequality Symbols
Inequality symbols are mathematical signs used to show the relationship between two numbers or expressions. The two most common symbols used are the greater than (\(>\)) and less than (\(<\)) signs.
These symbols indicate:
Being able to correctly use inequality symbols helps greatly in writing true mathematical statements and understanding relationships between numbers.
These symbols indicate:
- \(>\): The number before the symbol is greater than the number after.
- \(<\): The number before the symbol is less than the number after.
Being able to correctly use inequality symbols helps greatly in writing true mathematical statements and understanding relationships between numbers.