91Ó°ÊÓ

In algebra, one of the most fundamental tasks is isolating a variable. This means having the unknown variable, like \(y\) in our equation, on one side of the equation by itself. Why do we need to do this? Well, it helps us find the value of the variable step by step. In the given equation, \(6.9825 = 4.2296 + y\), \(y\) is not isolated because it is being added to 4.2296.
To isolate \(y\), we need to "undo" what is being done to it. Since it is being added to 4.2296, the opposite operation is subtraction. Thus, we subtract 4.2296 from both sides of the equation to keep it balanced.

• The equation becomes: \(6.9825 - 4.2296 = y\).
• By doing this, we are left with \(y\) on one side of the equation, isolated and ready to be calculated.

This concept is crucial because every operation done to one side of the equation must also be done to the other. Keeping equations balanced helps us find the exact value of the variable without errors.

Performing subtraction involves taking one number away from another. In our equation, we need to subtract 4.2296 from 6.9825. While this may seem straightforward, attention to detail is crucial to ensure there are no mistakes. Let's break down the subtraction step:

• Align the decimal points to ensure each digit is in its correct place value.
• Start subtracting from the rightmost digit, moving left towards the decimal point.
• In some cases, you might need to borrow from the next higher place value if the top digit is smaller than the bottom digit.

Our calculated difference will reveal the value we assign to \(y\). Using a calculator can help verify this manual calculation. In practice, consistent subtraction skills are necessary for solving more complex algebraic equations.

Using a calculator can be incredibly helpful, especially with decimal numbers, ensuring accuracy and saving time. If you're relatively new to using a calculator, here's a quick guide on making the most of it for subtraction problems like ours:

• Power on your calculator by pressing the appropriate button.
• Enter the first number (6.9825) into your calculator.
• Press the subtraction (−) button.
• Enter the second number to subtract (4.2296).
• Finish by pressing the equals (=) button to display the result.

This method ensures precise subtraction, reducing errors that might occur with manual calculations. Calculators are valuable tools, especially when checking work or tackling lengthy assignments. They are known for their accuracy and consistency, making them suitable companions for anyone learning math.