Solve for m:
$m - 21.1 = -36.6$
To solve for the variable \(m\) in the equation \(m - 21.1 = -36.6\), we need to isolate \(m\) on one side of the equation. This is a linear equation where \(m\) represents an unknown value. The goal is to determine which value, when reduced by \(21.1\), yields \(-36.6\).
To isolate \(m\), we use the addition property of equality, which states that adding the same number to both sides of an equation does not change the equality. Since we have \(-21.1\) on the left side, we add \(21.1\) to both sides of the equation to cancel it out:
\[m - 21.1 + 21.1 = -36.6 + 21.1\]
This simplifies the left side to \(m\):
\[m = -36.6 + 21.1\]
Now, we perform the addition of the constants on the right side:
\[-36.6 + 21.1 = -15.5\]
Therefore, the solution for the equation is:
\[m = -15.5\]
To verify, we can plug \(-15.5\) back into the original equation:
\[-15.5 - 21.1 = -36.6\]
The equality holds true, confirming our result. The final answer is \(\boxed{-15.5}\).
Linear equations like this are foundational for understanding how to balance simple budgets or track changes in values. For example, if your bank account has a balance of \(\$m\) and you make a withdrawal of \(\$21.10\), resulting in a new balance of \(-\$36.60\) (an overdraft), you can use this exact equation, \(m - 21.1 = -36.6\), to find your starting balance: \(m = \boxed{-15.5}\). This demonstrates how isolating variables helps reveal unknown starting points in various real-world financial or scientific scenarios.