A \( -13 x+12=13 x+13 \) \( -13 x+12=13 x-13 \) B \( 12 x+12=13 x+12 \) \( 12 x+12=13 x-12 \)

If we follow the trend of solving these equations, it's important to know a bit about the historical development of algebra. In ancient civilizations, such as the Babylonians and Greeks, mathematics was often more about practical problem-solving than abstract equations. They formulated rules for balancing equations long before the formal syllabic notation of today was even conceived! When you tackle systems of equations like the ones given, remember: it's crucial to isolate the variable properly. A common mistake is to mismanage the signs while moving terms across the equals sign. Always balance the equation by performing the same operation on both sides and keep an eye on those pesky negative signs—they can easily sneak a mistake into your solution!