Solve each equation for y.

$5x-2y=12$

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

In order to solve the given equation $5x-2y=12$ for the variable, isolate the variable term y on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate y on both sides, first subtract both sides by 5x.

$\begin{array}{c}5x-2y-5x=12-5x\\ -2y=12-5x\end{array}$

Now to further simplify divide both sides by 2.

$\begin{array}{c}-2y=12-5x\\ -\frac{2y}{2}=\frac{12-5x}{2}\\ -y=\frac{12-5x}{2}\\ -\left(-y\right)=-\left(\frac{12-5x}{2}\right)\\ y=\frac{5x-12}{2}\end{array}$