\( \left. \begin{array} { l }{ 3 x - ( 12 ) = - 4 x + ( 2 ) } \\ { + 4 x \quad + 4 x } \\ { \hline } \end{array} \right. \)

Let’s dive into the solution! First, we start with the equation \(3x - 12 = -4x + 2\). To make things easier, let’s move all the \(x\) terms to one side and the constant terms to the other side. If we add \(4x\) to both sides, we get: \(3x + 4x - 12 = 2\) Now, simplifying this gives us: \(7x - 12 = 2\) Next, add 12 to both sides: \(7x = 14\) Finally, divide by 7: \(x = 2\) And voila! We’ve solved the equation. If you're ever stuck solving equations, remember to keep your variables on one side and constants on the other. A common mistake is forgetting to balance both sides of the equation when you add or subtract, leading to incorrect answers. Always check if both sides are equal!