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- Solve for y and check your solution
- Twenty minus seven 'y' equals six 'y' minus six
- So what I really want to do is just isolate all of the 'y's on one side of the equation then if there's some sort of coefficient in front of it, I can divide both sides by that coefficient,
- and I can isolate the 'y' on either the left side or the right side of the equation.
- Actually let me do it both ways.
- So, first, let's... it looks like it'll be a little bit simpler if I isolate it on the right-hand side
- and I'll show you that in a second.
- So if I want to put all of the y's on the right
- hand side, how can I get rid of all the 'y's on the left-hand side?
- I have a minus seven 'y' or you can use the negative
- seven 'y'.
- I can add seven 'y' to both sides of this equation, so I'm just
- adding seven 'y' to both sides.
- Then the left hand side of the equation you have twenty minus seven 'y' plus seven y.
- Those are going to cancel out you're going to be just left with twenty.
- And on the right hand side of the equation
- you have six 'y' plus seven 'y' which is thirteen y.
- And then you have your minus six.
- And I want only 'y's or multiples of 'y's on the right hand side of the equation
- so I have to get rid of this minus six over here.
- So let's add six to both sides of this equation.
- Let's add six and then on the right hand
- side, I have thirteen 'y' minus six, plus
- six, that's just thirteen 'y'. Got rid of the minus.
- Then I have twenty plus six, so that's twenty-six. So I get twenty-six is equal to thirteen 'y'.
- I have isolated the 'y'
- on the right hand side although it's to be multiplied by thirteen.
- So if I just want a 'y'
- on the right hand side, one 'y' on the right hand side.
- I can divide both sides by thirteen.
- Or the equivalent statement would be to multiply both sides by one over thirteen, same thing.
- So let's divide both sides of this equation by thirteen.
- On the right-hand side, thirteen times 'y' divided by thirteen, that's just going to be 'y'.
- So this is just 'y'.
- And then twenty-six divided by thirteen
- that is two.
- So our solution we got is 'y' is equal to two.
- Now I'm going to take a step back, why did I say it was going to be a little easier to put the 'y'
- on the right hand side of the equation.
- That way I have a positive coefficient in terms of 'y'.
- If I had subtracted six 'y'
- from both sides, I would have got a negative thirteen on both sides, which would have been a legitimate t
- thing to do
- Let me just show you, what I'm talking about.
- So I could have done the problem this way:
- Twenty