Solving equations w/ Variables on both sides???

Question

For example, what are the steps for solving something like this?
8y-3=17-2y.
Is there a general set of steps for solving equations with variables on both sides? I'm really struggling with this.

Answer 1

Equations with variables on both sides require just one extra step then an equation with a variable on one side. The extra step would be choosing a variable on one of the sides and moving it to the other side. If you have a negative variable ( like -5x) you would add it to the other side. If you have a positive variable (like 4x) you would subtract it from the other side.

So for your problem: 8y-3=17-2y; you have a -2y on the right side. We can move that over to the left side as a positive 2y. So we would have: 8y+2y-3=17. Then we add the y's together and get 10y-3=17. Now we move the 3 over to the other side using the same rules (if negative, add to other side, if positive subtract from other side). Since the 3 is negative, we add it to the 17: 10y=17+3 _--> 10y=20. Now you know we have to isolate the variable and that means dividing each side by 10 and that leaves you with y=2! If you need more help, feel free to e-mail me.

Answer 2

Solve 2(4y - 5) + 7 = 8 - y + 9 - y.

Step 1 Apply the distributive law.
8y - 10 + 7 = 8 - y + 9 - y

Step 2 Combine like terms.
8y - 3 = 17 - 2y

Step 3 Choose the term with the variable that has the smallest coefficient. In this case, -2y. Add the opposite of -2y to both sides of the equation.
8y + 2y - 3 = 17 - 2y + 2y
and
10y - 3 = 17

Step 4 Add the opposite of any term, that is on the same side of the equation as the term with the variable, to both sides of the equation.
10y - 3 + 3 = 17 + 3
and
10y = 20
and
y = 2

Answer 3

whenever solving ANY equation your goal is to isolate the unknown. however, if you have a variable on both sides oh the equation before you isolate the unknown, you should combine like terms:

8y - 3 = 17 - 2y
8y - 3 + 2y = 17 - 2y + 2y
10y - 3 = 17
10y - 3 + 3 = 17 + 3
10y = 20

Now you can isolate the variable by performing the opposite operation:
y = 20/10 or y = 2

Answer 4

just transpose.

move terms with the same variable on one side then solve..

in your example,
8y-3=17-2y
8y+2y=17+3
10y=20
y=2

Answer 5

get the variables on one side. with that example, add the 2y to both sides so you get 10y-3=17. then you know what to do from there?

Answer 6

Oh, very easy, move the y's to one side, and the numbers to the other.

Then multiply both sides or divide both sides or a combination to get y by itself.

In this problem, first add 2y to both sides, then add 3 to both sides.

10y = 20

10y is positive, so there is no need to multiply by -1.
Simply divide both sides by 10.

y = 2

Piece of cake.

Answer 7

8y-3 = 17 -2y
first add 2y to both sides.
10y - 3 = 17
then add 3 to both sides.
10y= 20
divide both sides by10
y =2