Solve. \[ y+3=2 y-9 \]

To solve the equation \( y + 3 = 2y - 9 \), we first isolate \( y \). 1. Subtract \( y \) from both sides: \[ 3 = y - 9 \] 2. Then, add 9 to both sides: \[ 3 + 9 = y \] \[ y = 12 \] So, the solution to the equation is \( y = 12 \). Now for some fun insights! You might find it interesting to know that algebra, the branch of mathematics responsible for equations like this one, has its roots in ancient civilizations such as the Babylonians over 4,000 years ago. They utilized a form of algebra that dealt with solving equations, much like the work we do today, but in a very different way that didn't use variables as we know them now. In practical terms, solving equations like this is essential not just in mathematics but in fields like engineering and finance. For example, if you're designing a bridge, you'll need to solve various equations to ensure the structure can support certain weights, making it a lifesaver (quite literally!) for structural integrity and safety.