Problem 41 - Elementary and Intermediate Algebra

Question

Write a true sentence using either \(< or >\) $$ 7 \square 0 $$

Step-by-Step Solution

Answer

7 > 0

Step 1: Understand the Symbols

The symbols '<' and '>' are used to compare two numbers. '<' means 'less than' and '>' means 'greater than.'

Step 2: Compare the Given Numbers

We need to compare the two numbers 7 and 0. Determine which of these is larger.

Step 3: Write the True Sentence

Since 7 is greater than 0, the correct symbol to use is '>'. Therefore, the correct sentence is: o o 7 > 0

Key Concepts

inequalities

In mathematics, inequalities are statements that compare two values, showing if one is larger, smaller, or possibly equal to the other.
Unlike equations, which show that two expressions are equal, inequalities use symbols like '<' (less than), '>' (greater than), '≤' (less than or equal to), and '≥' (greater than or equal to) to represent this relationship.
Inequalities are very useful in a variety of mathematical contexts, from solving problems in algebra to analyzing data.
When comparing two numbers, these symbols help us understand the relationship between them at a glance.

greater than

The 'greater than' symbol is represented by '>'.
When we say one number is greater than another, it means that the first number is larger.
For example, in the exercise provided: 7 compared to 0, we need to determine if 7 is larger than 0.

• If the first number is larger, we use the '>' symbol.
• This helps to quickly understand the comparative size of the numbers.

In this example 7 > 0 is the true statement, indicating that 7 is indeed greater than 0.
Visually, you can think of the '>' symbol as an alligator's mouth that prefers to eat the larger number on its open side.

less than

The 'less than' symbol is represented by '<'.
When saying one number is less than another, it means that the first number is smaller than the second.

• If the first number is smaller, we use the '<' symbol.
• This makes it easy to understand how the numbers compare.

In our original exercise comparing 7 and 0:
We noted that 7 is greater, so the use of '>' is appropriate. However, if the comparison was reversed, such as in 0 < 7, the '<' symbol shows that 0 is less than 7. This clear distinction helps avoid confusion when working with comparative problems.