Solving Equations with Variables on Both Sides Examples

Solve for y:

In this equation we need to first distribute the 5 and then get the y's on one side. They love their privacy.

	distribute the 5
	subtract 5y from each side
	combine the like terms
	subtract 2 from each side
	simplify
	divide each side by -2
	high-five yourself

Now we check it:

Solve for k:

We threw this one in here to keep you on your toes. At first glance it looks like all the variables are on the left side. However, when you multiply each side by k (to get the variable out of the denominator), there will be variables on each side.

	multiply each side by k
	the k's on the left cancel
	subtract 2k from each side
	simplify
	divide each side by 2

Check!

Solve for y:

14x – 3y + m = -12m – 3x – 4y

We start by moving all of the terms without a y to the right of the equal sign. So we subtract 14x and subtract m.

(14x – 3y + m) – 14x – m = (-12m – 3x – 4y) – 14x – m
-3y = -13m – 17x – 4y

Now we move the y terms all to the left side of the equal sign by adding a 4y.

(-3y) + 4y = (-13m – 17x – 4y) + 4y
y = -13m – 17x

y is now all alone on the left of the equal sign—it's lonely at the top (or on the left)—and we've solved for y.