Solve using the addition principle. Don't forget to perform a check. \( \begin{array}{l}9+x=12\end{array} \)

To solve the equation \(9 + x = 12\) using the addition principle, we want to isolate \(x\). To do this, we can subtract 9 from both sides of the equation: \[ 9 + x - 9 = 12 - 9 \] This simplifies to: \[ x = 3 \] Now, let's perform a quick check by substituting \(x\) back into the original equation: \[ 9 + 3 = 12 \] Since both sides are equal, our solution \(x = 3\) is correct! Furthermore, the addition principle states that you can add or subtract the same number from both sides of an equation without changing its equality. This principle is widely used in algebra to manipulate equations to isolate variables effectively. In real-world applications, understanding how to isolate variables can help you with everyday situations—like budgeting. For instance, if you know your expenses and total income, isolating the unknown savings or spending helps you make better financial decisions!