Verified Answer :

  • The given equation is \(-6n = 72\).
  • To isolate \(n\), divide both sides of the equation by \(-6\).
  • The division \(\frac{72}{-6}\) results in \(n = -12\).
  • The final answer is \(\boxed{-12}\).

Explanation

  1. Analysis of the Equation

The given equation is \(-6n = 72\), where \(n\) is the variable we want to find. The equation involves multiplying \(n\) by \(-6\). To isolate \(n\), we need to perform the inverse operation, which is division. Dividing both sides of the equation by \(-6\) will allow us to solve for \(n\).

  1. Solving for n

To solve for \(n\), we divide both sides by \(-6\):
\[n = \frac{72}{-6}\]
Performing the division, we find:
\[n = -12\]
Thus, the value of \(n\) that satisfies the equation is \(-12\).

Examples

Imagine you are playing a game where your score is multiplied by -6 every round. If your current total score is 72, you can use the equation \(-6n = 72\) to find out how many rounds (\(n\)) it took to reach that score, where \(n\) represents a negative value. Solving for \(n\) helps you determine the history of your score changes in this context. Algebra allows us to calculate unknown factors in various real-life scenarios like finance, physics, or game design.

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