Isolating the Variable, Part Deux
Or, “How to see a variable naked when there are other variables in the room.”
Sometimes your equation will have more than one variable in it. It will look something like this:
4x + 7y - z = 42 Think of the stuff on each side of the equal sign as being in different rooms.
You still want to see X naked, but now he’s not just wearing stuff, but 7 people named Y and a really negative punk named Z are standing in the way. You’ve got some work to do. Unfortunately, in Math, you can’t just make these Y and Z people evaporate. But you can make them go to the other room and do things to make your equation look like this:
X = something.
And that’s what we want. To get X alone. Isolated. And naked. So let’s get down to business.
First, let’s get Z to leave the room. Z got into the room by subtraction (our expression is “-z”), so to undo that, we’ll have to add:
4x + 7y – z = 42
4x + 7y –z + z = 42 + z
4x + 7y + 0 = 42 +z or 4x + 7y = 42 + z
Now let’s kick out the Y peeps. There were 7 of them added here, so let’s subtract 7 of them from both sides:
4x + 7y = 42 + z
4x + 7y -7y = 42 + z – 7y
4x + 0 = 42 + z – 7y
4x = 42 + z – 7y
Whew! All that’s left in the room is X, wearing those pesky 4 shirts. No matter. We can tear them off his body. He put them on via multiplication (4 times x), so all we have to do is divide:
4x = 42 + z – 7y
4x/4 =42 + z – 7y
X = 42 + z – 7y
Yes. That does look like a mess. X is kind of a mess. But you’re forgetting– he’s naked! That’s what we wanted. That’s what we asked for.
It’s important to be careful what you ask for. Sometimes when you get it, you find out that it isn’t as attractive as you originally thought it would be.