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When solving a linear equation like \(7.68y = -114.98496\), our main objective is to find the value of the variable \(y\). This process is known as isolating the variable. It involves manipulating the equation until the variable is left alone on one side.

• Identify the variable to be isolated, which in this case is \(y\).
• Determine what is being done to \(y\) (e.g., multiplied by a coefficient), and the aim is to undo this operation to solve for the variable.

In the equation given, the variable \(y\) is being multiplied by \(7.68\). To isolate \(y\), you'll need to perform the opposite operation, which means dividing both sides of the equation by \(7.68\). This clears \(7.68\) from beside \(y\) and leaves us with \(y = \frac{-114.98496}{7.68}\).
Through this process, isolating a variable becomes a systematic approach to simplify and solve equations, turning even the most challenging problems into a series of methodical steps.

In algebra, division is often used to simplify equations, especially for isolating a variable. Let's dive into its application in our problem:
Why Use Division?- Division is the inverse operation of multiplication.- It helps in removing coefficients (numbers next to variables) that may be impeding the isolation of a variable.
In our example, the equation \(7.68y = -114.98496\) involves rearranging to solve for \(y\). Divide both sides by \(7.68\) to break the multiplication attaching \(7.68\) to \(y\). The division is conducted as follows:\[ y = \frac{-114.98496}{7.68} \]Perform this computation to get the value of \(y\), which is \(-14.98496\) in this instance. Using division in algebra ensures that calculations remain correct and balanced, achieving an accurate solution.

Once you've isolated the variable and obtained a solution, it is crucial to verify it. Verification ensures the solution is correct and the initial equation's integrity is maintained.
How to Verify a Solution:

• Substitute the calculated variable value back into the original equation.
• Check if both sides of the equation still hold true.

For our problem, substitute \(y = -14.98496\) back into the original equation \(7.68y = -114.98496\). Calculate:\[ 7.68(-14.98496) = -114.98496 \]Since both sides of the equation are equal, this confirms that the calculated value for \(y\) is indeed correct. Verifying solutions is a critical step as it reconfirms your calculations and provides confidence in the solution.