Question

Solve each equation for y.

$3-\frac{1}{2}y=5x$

Short answer

The equation for y is $y=6-10x$.

Step-by-step solution

Step 1. State the concept used.

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

Step 2. Rewrite the equation to solve for y.

In order to solve the given equation$3-\frac{1}{2}y=5x$for the variable, isolate the variable term yon one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolateyon both sides, first subtract 3 from both sides.

$\begin{array}{c}3-\frac{1}{2}y-3=5x-3\\ -\frac{1}{2}y=5x-3\end{array}$

Step 3. Simplify further for y.

Now to further simplify multiply both sides by 2.

$\begin{array}{c}-\frac{1}{2}y\times 2=\left(5x-3\right)\times 2\\ -y=10x-6\\ -\left(-y\right)=-\left(10x-6\right)\\ y=6-10x\end{array}$