2. 5 olve for \( y: 5 y-4=2 y+8 \)

To solve for \( y \) in the equation \( 5y - 4 = 2y + 8 \), start by isolating the variable on one side. First, subtract \( 2y \) from both sides: \[ 5y - 2y - 4 = 8 \] This simplifies to: \[ 3y - 4 = 8 \] Next, add 4 to both sides: \[ 3y = 12 \] Finally, divide each side by 3 to solve for \( y \): \[ y = 4 \] So, the solution is \( y = 4 \). Now let's dive into some additional insights! One cool fact about equations like this is that they're part of algebra, which has roots dating back thousands of years to ancient Babylonian mathematicians who developed methods to solve linear equations. It’s fascinating to think how these principles have remained relevant throughout history! If you're tackling similar equations, a common mistake is forgetting to perform the same operation on both sides of the equation. Always remember to maintain balance - if you add, subtract, multiply, or divide on one side, do the same to the other side to keep your equation true!