Question

Use \(<\) or \(>\) to write a true statement. $$-12 ?-19$$

Short answer

Question: Determine the correct comparison statement for the numbers -12 and -19 using either \< or \>. Answer: -12 > -19

Step-by-step solution

Compare the numbers

Given the numbers -12 and -19, we know that -12 is closer to 0 than -19. Therefore, -12 is greater than -19.

Write a true statement

Since -12 is greater than -19, the true statement using either \(<\) or \(>\) is: $$-12 > -19$$

Key concepts

Comparing Negative Numbers

When dealing with negative numbers, it's important to remember that they function differently from positive numbers. The number line helps us understand this better. The further to the right a number is, the greater its value.
This rule applies to negative numbers as well. So,

• The closer a negative number is to zero, the greater it is.
• The more negative a number is, the smaller it is compared to less negative numbers.

For example, when comparing i\(-12\)i and i\(-19\)i, you may notice that i\(-12\)i is closer to zero.
Thus, i\(-12\)i is greater than i\(-19\)i.

Greater Than

The concept of 'greater than' (\(>\)) is fundamental in comparing numbers. When you say one number is greater than another, you are saying it is larger or higher in value.
For positive numbers, this is straightforward, as larger numbers mean more.
But when dealing with negative numbers, remember:

• The closer a negative number is to zero, the greater it is.
• i\(-12 > -19\)i because i\(-12\)i is less negative than i\(-19\)i.

Being able to identify and apply this principle will help you correctly compare both negative and positive numbers in various mathematical situations.

Inequality Symbols

Inequality symbols such as \(>\) and \(<\) are used to compare numbers, determining which is greater or smaller. An inequality symbol helps express the relationship between two numbers:

• The \(>\) symbol means 'greater than.'
• The \(<\) symbol means 'less than.'

In the example i\(-12 > -19\)i:

• i\(>\)i represents the fact thati\(-12\)i is greater.
• This is because i\(-12\)i is closer to zero on the number line compared to i\(-19\)i.

Understanding how to properly use these symbols is key to accurately solving inequalities and expressing the relationship between numbers.