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Chapter 2: Problem 46

Use \(<\) or \(>\) to write a true statement. $$-14 ?-11$$

Short Answer

Expert verified
Answer: -14 is less than -11.

Step by step solution

01

Understand the inequality symbols

The symbols < (less than) and > (greater than) are used to compare two numbers. - When a number is smaller than the other number, the symbol < will be used: A < B - When a number is larger than the other number, the symbol > will be used: A > B Remember that when dealing with negative numbers, the values increase in the opposite direction. So, for negative numbers, the smaller number has the greater value.
02

Compare the given numbers

Now, let's compare the two given numbers -14 and -11. On the number line, -14 is to the left of -11. Keeping in mind that the values increase in the opposite direction for negative numbers, we can conclude that -14 is less than -11.
03

Write the true statement

Using the proper inequality symbol, we can write the true statement as: $$-14<-11$$

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Key Concepts

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

Inequality Symbols
In mathematics, inequality symbols are crucial for comparing two numbers. There are two main symbols you need to know:
  • \(<\), meaning "less than"
  • \(>\), meaning "greater than"
When you see a \(<\) symbol between two numbers, it indicates that the first number is smaller than the second.
Conversely, a \(>\) symbol shows that the first number is larger. This basic concept is usually easy to understand with positive numbers. However, it can be a bit trickier with negative numbers, which we will explain in the next section. Keep these symbols in mind as they are key to writing and understanding mathematical statements.
Negative Numbers Comparison
Comparing negative numbers might seem complicated at first. But once you grasp the unique nature of negative values, it's quite straightforward.
Here's the key idea: on a number line, the further left you go, the smaller the number's value. In terms of negative numbers, a number that appears to be smaller is actually larger.
For example, consider -14 and -11. Although 14 is greater than 11 in positive terms,
  • -14 is smaller than -11 because it is further to the left on the number line.
  • This means \(-14 < -11\).
This reversal of the usual number order confuses many. Remember, the more negative a number, the smaller it is. Comparing negatives becomes simpler with this perspective!
Number Line Interpretation
Interpreting a number line helps visualize number relationships, especially with negative values.
Imagine the number line running horizontally, with zero at the center. Positive numbers are found on the right, negative numbers on the left.
  • The further to the right a number is, the greater its value.
  • The further to the left, the smaller its value.
With negative numbers, you see that for numbers like -14 and -11, -11 is closer to zero. This means -11 holds a higher value than -14 because it is less "negative."
When tackling number line questions, remember position indicates value, moving from smaller to larger as you approach zero from the left.

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