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hmm, we'll your not quite right 1st of all, so let me correct you.

3(y-2) + 2y = 4y + 14

So the parenthesis (y-2) are multiplying with the 3

in order to multiply these 3(y-2) you use the distribution property, like you said.

and you get

(3*y - 3*2) + 2y = 4y + 14

the main difference is because that last 2y wasn't in the parenthesis, it gets exiled from the distribution process. Also you don't multiply the other side by 3 either in the distribution process. Only what's in the parenthesis.

So you get

3y - 6 + 2y = 4y + 14

and combine like terms

5y - 6 = 4y + 14

then to deal with this, the idea is you want to isolate y all by itself on one side of the equation. So to do this you want to move the stuff involving y to one side, and the stuff not involving y to the other side.

Ok so how do we do that?

5y - 6 = 4y + 14

Let start by moving the -6 from the left side of the equation to the right side. It would be great if that -6 was a 0, so that we wouldn't have to worry about it any more. Lets just make it 0 then! Add 6 to the left side and it will be 0

5y - 6 +6 = 4y + 14

exclaim but we just changed the equation, which is bad. So how do we fix it? Well the fundamental rule of algebra is, in order to keep the sides the same, do the same thing to /both/ sides of the equation. For instance. If I told you that 2=2, that would be true. Now I say I want that 2 to be a 0, so I subtract 2 from the left side. (2-2)=2. And you would get 0=2 which is no longer true. So to fix it you just do the same thing to both sides. So if I subtracted 2 from the left side, I better do it to the right side too. So you get (2-2)=(2-2), which is 0=0 which is still true! So as long as you do the same thing to both sides the equation will be true.

so we added 6 to the left side, so we add it to the right side

5y - 6 +6 = 4y + 14 +6

combine like terms

5y +0 =4y + 20

the 0 is unimportant, so we don't need to write it

5y = 4y + 20

ok lets move the 4y from the right side to the left. We want to make it 0, so subtract 4y from the right side. And since we're doing that to the right side, we better do it to the left.

5y -4y = 4y + 20 -4y

combine like terms

y=0y+20

again the 0y is unimportant so we don't write it

and you get

y=20

now check your work!

plug in y =20 back into your original equation. So every time you see a y substitute it for 20

3(y-2) + 2*y = 4*y + 14

3(20-2) + 2*20 = 4*20 + 14

lets do the math!

3(18 ) + 40 = 80 + 14

54 + 40 = 94

94 = 94

Yay! So your done, any questions?