Solve for $g$.
$\begin{array}{l}
112=g-400 \\
g=
\end{array}$
The objective is to find the value of the variable \(g\) in the equation \(112 = g - 400\). To isolate \(g\), we need to eliminate the constant term \(-400\) on the right-hand side of the equation. We can achieve this by performing the same operation on both sides of the equation.
To isolate \(g\), we add \(400\) to both sides of the equation:
\[112 + 400 = (g - 400) + 400\]
This simplifies the equation to:
\[112 + 400 = g\]
Now, we perform the addition to find the value of \(g\):
\[g = 512\]
Thus, the value that satisfies the given equation is \(512\).
Suppose you are tracking your total savings in a bank account. You know that if you withdraw \(\$400\), your remaining balance will be \(\$112\). To find your initial balance \(g\), you can set up the equation \(112 = g - 400\). By adding the \(\$400\) back to the current balance, you determine that you started with \(\$512\). Understanding how to isolate variables is a fundamental skill for managing finances, planning budgets, and solving many real-world problems involving missing quantities.