91Ó°ÊÓ

To solve a linear equation, the first step is to isolate the variable. This means getting the variable, in this case, \(z\), by itself on one side of the equation. Think of it like solving a puzzle; you want to separate \(z\) from the other numbers. Isolating the variable simplifies the equation, making it easier to find the value of \(z\). To do this, you'll need to use basic arithmetic operations, like addition, subtraction, multiplication, or division. Whenever you perform any operation on one side, you must do the same on the other side to maintain balance. For example, if we have the equation \(512 - 63 = z\), we want to perform operations that will leave \(z\) alone on one side.

Subtraction is a common operation used to isolate the variable in an equation. In the given equation \(512 - 63 = z\), subtraction helps to remove numbers from around the variable. Here, subtracting 63 from 512 directly gives us the value of \(z\). Remember to line up your numbers correctly if you're doing the subtraction by hand: 512 minus 63. Always double-check your work to ensure that the subtraction was completed accurately:

• Start with larger number: 512
• Subtract smaller number: 63
• Result: 512 - 63 = 449

This gives us \(z = 449\). Subtraction simplifies the equation, bringing you closer to the solution.

Once you've isolated the variable and found its value, the next crucial step is checking the solution. Verifying your answer ensures that your solution is correct. To check, substitute the value back into the original equation. For the equation we solved, substitute \(z = 449\). So, reinserting \(449\) into the original equation, we get:

• Original equation: 512 - 63 = z
• Substitute z: 512 - 63 = 449

If both sides of the equation are equal, then the value you found is the correct solution: Yes, 512 - 63 does indeed equal 449. This confirmation step is essential to ensure the reliability and correctness of your solution.