This is probably a stupid question basic equation laws

[dvmckay23]

Okay, so say I have an equation that looks like this:

9y - 4x + 5 = 0
and I wan to move every thing but the y over to the right hand side.

When it gets to the last step and looks like this:
9y = 4x - 5

When I move 9 over to the other side, does it's sign change? I know the other terms will be divided by it, but I don't remember if it is supposed to be negative... my text has examples that aren't quite clear.

Thanks!

 

[Borek]

$$y = \frac {4x - 5} {9}$$

To move 5 from the left to right you have substracted 5 from both sides - in effect it has changed the sign, but all you did was to make the same operation to both sides of the equation.

To move 9 to the right side you have to divide both sides by 9. Sign won't change, but 9 will move from nominator to denominator. In a way that's similar to sign change.

 

[HallsofIvy]

This is why I strongly dislike talking about moving numbers from one side of the equation to the other! People get confused about changing sign because "moving" doesn't distinguish between add and dividing.

When you "move" the x in x+ y= 5 to the right, what you are really doing is subtracting x from both sides of the equation. You should be thinking, "the x in x+ y is added to y so I need to do the opposite, subtract it from both sides:
x+ y- x= 5- x which reduces to y= 5- x. x didn't "change sign", it is subtracted.

If you have xy= 5 and want to get y alone, because x is multiplied, again you have to do the opposite: divide. xy/x= 5/x which is just y= 5/x.

 

[Diffy]

Halls, great answer. It is so important that teachers of algebra pay particular attention to what they say they are doing, and their language. They then need to impose the same strictness on their students. (Easier said then done, I know, but in a perfect world...). "Moving a number to the other side" is way to ambiguous for mathematics. This causes students to get confused; case and point the OP.