\( \frac{3 y-2}{4}+1=5 \) Find the value of \( y \)

To solve the equation \( \frac{3y - 2}{4} + 1 = 5 \), we start by isolating the fraction. First, subtract 1 from both sides: \[ \frac{3y - 2}{4} = 4 \] Next, we multiply both sides by 4 to eliminate the fraction: \[ 3y - 2 = 16 \] Adding 2 to both sides gives: \[ 3y = 18 \] Finally, divide both sides by 3: \[ y = 6 \] So, the value of \( y \) is \( 6 \). Now, let's explore some fun facts! Did you know that algebra has roots that can be traced back to ancient civilizations such as the Babylonians? They were already solving linear equations over 3,500 years ago using geometric methods which laid the groundwork for modern algebra! In real-world applications, algebra is everywhere, from calculating expenses in a budget to analyzing data trends in business. For instance, a company may use algebraic equations to predict future sales based on current trends, helping them make informed decisions. It's all about using those "y"s and "x"s to navigate life intelligently!