Solve for $f$.
$f + 47 = -26$
$f + 47 = -26$
Solve for $f$.
$f + 47 = -26$
The objective is to solve the linear equation for the variable \(f\). The given equation is:
\[f + 47 = -26\]
To isolate the variable \(f\), we need to perform the same arithmetic operation on both sides of the equation to neutralize the term added to \(f\).
To isolate \(f\), we subtract 47 from both sides of the equation:
\[f + 47 - 47 = -26 - 47\]
This simplifies to:
\[f = -26 - 47\]
Now, we perform the subtraction on the right-hand side. Since both numbers are negative, we add their absolute values and keep the negative sign:
\[-(26 + 47) = -73\]
Therefore, the value of \(f\) is \(-73\).
We have successfully solved for \(f\) and determined that the value is \(-73\). Plugging this value back into the original equation, we get \(-73 + 47 = -26\), which confirms our result. Thus, \(f = \boxed{-73}\).
Solving for a variable in a simple linear equation is a foundational skill in algebra. For example, if you have a budget of \$100 and you have already spent \$47 on supplies, you can represent the remaining balance \(f\) with the equation \(f + 47 = 100\). By using the same isolation method, you can easily calculate that your remaining budget is \(100 - 47 = 53\). This logic applies to countless real-world scenarios involving managing resources, tracking debts, or adjusting quantities.