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Chapter 2: Problem 45

Use \(<\) or \(>\) to write a true statement. $$-19 ?-17$$

Short Answer

Expert verified
Question: Use the less than ('\(<\)') or greater than ('\(>\)') symbol to create a true statement comparing the numbers -19 and -17. Answer: $$-19 < -17$$

Step by step solution

01

Compare the numbers

Determine the relationship between the two numbers. -19 and -17 are negative numbers. In a number line, negative numbers increase in value as they approach zero. Therefore, -19 is to the left of -17 on the number line, making it smaller than -17.
02

Choose the appropriate symbol

Since -19 is smaller than -17, we will use the less than ('\(<\)') symbol to create a true statement.
03

Write the true statement

The true statement comparing the two numbers -19 and -17, using the less than ('\(<\)') symbol is: $$-19 < -17$$

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Key Concepts

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

Number Line
A number line is a visual representation of numbers arranged in an increasing order from left to right. It helps us to easily compare and understand the value of different numbers, including negative numbers.
  • The left side of the number line contains negative numbers.
  • The zero point is the center of the number line.
  • As we move right from zero, numbers become positive and increase in value.
Understanding the number line is crucial when working with negative numbers. On the left of zero, numbers become more negative and thus, are smaller. This means that on the number line, a number further left is smaller, and a number further right is larger. For instance, -19 is placed to the left of -17, indicating that it is less than -17.
Inequalities
Inequalities are mathematical expressions used to show the relationship between two values. They tell us if one number is smaller, greater, or even equal to another number. Common symbols include:
  • Meaning "less than"
  • meaning "greater than"
Using inequalities is essential when comparing numbers, especially negatives, where visualizing the relationship can be tricky. For example, -19 being smaller than -17 is expressed using the inequality symbol ' '. Thus, -19 < -17. This inequality tells us that -19 is less than -17, providing a clear and succinct depiction of their relationship.
Negative Values
Negative values are numbers less than zero and are crucial in real-world applications and mathematics. They represent many concepts like debt, temperature below zero, or points below sea level.
  • Negative numbers are found to the left of zero on the number line.
  • Their value decreases as they move further from zero.
  • A larger negative number (like -19) is actually less than a smaller negative number (like -17).
Understanding negative values requires a mental shift from how we usually perceive numbers. Larger negative numbers appear smaller in value because they represent a greater deviation below zero. For example, when you compare -19 and -17, -19 is the smaller value because it is further from zero. Recognizing this concept is essential for solving equations and inequalities involving negative numbers.

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