- Identify the equation: \(6m = -36\).
- Divide both sides by 6 to isolate \(m\).
- Calculate the result: \(m = \frac{-36}{6}\).
- Final result: \(\boxed{-6}\).
Explanation
- Problem Analysis
We are given the linear equation \(6m = -36\). Our goal is to isolate the variable \(m\) to find its value. In this equation, \(m\) is multiplied by a coefficient of 6. To solve for \(m\), we need to perform the inverse operation, which is division, to isolate the variable on one side of the equation.
- Solving the Equation for \(m\)
To isolate \(m\), we divide both sides of the equation by 6:
\[6m \div 6 = -36 \div 6\]
This simplifies the left side to \(m\) and allows us to compute the value on the right side. Performing the division \( -36 \div 6 \), we get:
\[m = -6\]
Thus, the value of \(m\) that satisfies the equation is \(-6\).
Examples
Imagine you are tracking your bank balance, and you have set up an automatic payment plan where you lose \(\$6\) from your account every day for a specific number of days. If your balance has decreased by a total of \(\$36\) over that period, you can find the number of days, \(m\), by solving \(6m = 36\). In our case, with the equation \(6m = -36\), this model helps in understanding how debts or withdrawals are represented mathematically and how to solve for unknown time intervals or quantities.