Problem 42 - Elementary Algebra

Question

Fill in the blank with \(<,=,\) or \(\geqslant\). 30 _____ 2

Step-by-Step Solution

Answer

30 > 2.

Step 1: Understand the Problem

We need to compare the number 30 with the number 2, and determine which mathematical operator appropriately fills the blank: less than ( < ), equals (=), or greater than or equal to ( geqslant ).

Step 2: Compare the Numbers

To fill in the blank, we compare the size of the numbers. Since 30 is greater than 2, we use the 'greater than' symbol.

Step 3: Choose the Correct Symbol

Based on our comparison, 30 is greater than 2, so the correct operator is 'greater than', denoted by '>.' However, as 'geqslant' was an option, 30 is indeed greater or equal to 2.

Step 4: Fill in the Blank

Fill in the blank with the chosen operator: 30 ext{ extgreater } 2 as 30 is greater than 2.

Key Concepts

Comparison of Numbers

In elementary algebra, comparing numbers is a fundamental concept. Numbers can be compared to determine which is larger, smaller, or if they are equal. When you compare numbers like 30 and 2, you assess their values to see which number holds a greater value.

• Greater Than: In the comparison of numbers, if you find that one number is larger than another, it is labeled as 'greater than'.
• Less Than: Conversely, if one number is smaller, it is termed as 'less than'.
• Equal To: If the numbers are the same, they are considered 'equal to'.

Through the example problem, you see that 30 possesses a larger value than 2, clearly indicating that 30 is greater than 2. This is a valuable skill as it lays the foundation for understanding more complex mathematical concepts.

Inequality Symbols

Inequality symbols are crucial tools in math that help us describe relationships between numbers.

• '<' - This symbol indicates that the number on the left is less than the number on the right.
• '=') - The symbol signifies equality, meaning both numbers are the same.
• '\(\geqslant\)' - This symbol shows that the number on the left is greater than or equal to the number on the right.

These symbols allow us to efficiently communicate mathematical ideas. In the original exercise, the symbol '\(\geqslant\)' is appropriate as it includes both greater than and equal possibilities, reflecting that 30 is indeed greater than 2.

Problem-Solving Steps

Approaching problem-solving in algebra requires a series of logical steps to reach a solution:

• Step 1: Understand the problem: First, identify what you're being asked. In this case, it's to decide which symbol fills the blank appropriately.
• Step 2: Compare the numbers: Evaluate the numbers you are given. Here, you determine that 30 is greater than 2.
• Step 3: Choose the correct symbol: Based on your comparison, you would then select the most fitting inequality symbol. Given that 30 is greater, '\(\geqslant\)' is used.
• Step 4: Fill in the blank: Finally, insert the correct symbol to complete the mathematical statement, resulting in 30 \(\geqslant\) 2.

Using these steps ensures a structured approach, making problem-solving clearer and more effective. By breaking it down, you engage in a step-by-step thought process, facilitating better understanding and practice.