- Identify the equation: \(f + 47 = -26\).
- Isolate the variable \(f\) by subtracting 47 from both sides: \(f = -26 - 47\).
- Compute the final value: \(f = -73\).
- The final answer is \(\boxed{-73}\).
Explanation
- Understanding the Problem
The problem asks us to solve the linear equation \(f + 47 = -26\) for the unknown variable \(f\). Our goal is to isolate \(f\) by moving all constant terms to the other side of the equation using basic algebraic properties.
- Isolating the Variable f
To isolate \(f\), we need to perform the inverse operation of adding 47. By subtracting 47 from both sides of the equation, we get:
\[f + 47 - 47 = -26 - 47\]
This simplifies to:
\[f = -26 - 47\]
- Calculating the Result
Now we calculate the sum on the right-hand side. Since both numbers are negative, we add their absolute values and maintain the negative sign:
\[f = -(26 + 47) = -73\]
Thus, the value that satisfies the given equation is \(f = -73\).
Examples
This type of equation represents simple balancing. For example, if you have a bank account with an overdraft limit and you need to determine the starting balance \(f\) such that adding a credit of 47 leaves you with a balance of -26, you can model it as \(f + 47 = -26\). Solving this shows that you must have started with a debt of 73, or \(f = -73\). Understanding linear equations allows you to calculate missing values in financial, scientific, and daily tasks.