91Ó°ÊÓ

Isolating the variable is the first crucial step in solving equations. The goal is to get the variable by itself on one side of the equation.
In the given exercise, we start with the equation \( 6y + \frac{1}{2} = 5y \). The variable here is y.
To isolate y, we need to move all terms containing y to one side. We do this by subtracting 5y from both sides since subtraction keeps the equation balanced. This operation helps in isolating the variable effectively.
After subtraction, the equation transforms to \( 6y - 5y + \frac{1}{2} = 0 \). This is key for making the equation easier to solve.

Simplifying equations is about combining like terms and making the equation easier to manage.
From the previous step, our equation is \( 6y - 5y + \frac{1}{2} = 0 \). We see two terms with y and one constant term. By combining the like terms (6y - 5y), we simplify the equation to \( y + \frac{1}{2} = 0 \).
This new, simpler equation makes it clearer what next steps we need to take to solve for y.
Always combine like terms and simplify step-by-step to avoid mistakes and to keep the process organized.
This step is pivotal and ensures errors are minimized while keeping the equation as simple as possible.

Equations with variables on both sides may seem tricky at first, but they follow a straightforward process.
We start with \( 6y + \frac{1}{2} = 5y \), where y is on both sides of the equation. The key here is to bring all terms involving the variable to one side and constants to the other.
As shown, by subtracting 5y from both sides, we have \( 6y - 5y + \frac{1}{2} = 0 \), reducing the equation to a simpler form \( y + \frac{1}{2} = 0 \).
Finally, we solve for y by subtracting \( \frac{1}{2} \) from both sides to get \( y = - \frac{1}{2} \).
Following these steps ensures you balance the equation properly and isolate the variable to find a solution.
Remember, practice makes perfect. The more you work with such equations, the more comfortable you'll become!