   SEARCH HOME Math Central Quandaries & Queries  Question from erin, a student: z+81=9z-7 Erin,

You can think of equations as twin children. To be fair, what you do with one you should do with the other. So in an equation, whatever you do to one side of the equal sign, you should do to the other.

Let me show you how this is done in a question similar to yours:

Solve 2x + 17 = 5x - 16.

The job is to get just one x by itself on one side of the equal sign (it doesn't matter which side, but we usually like to put the unknown on the left). So we want x = ?.

We want to remove any x terms from the right side, so we'll remove the 5x from the right hand side. What do we have to do to remove it? We can subtract 5x. So we have to do that to both sides (to keep it fair and equal).

2x + 17 - 5x = 5x - 16 - 5x

This simplifies:

2x - 5x + 17 = 5x - 5x - 16

-3x + 17 = -16

Next, we want to remove any terms without an x in them from the left side. So we can subtract 17 from both sides:

-3x + 17 - 17 = -16 - 17
-3x = -33

Last, we remove the factor -3 from the term on the left side. This is a factor though, so to remove it and leave the x behind, we can divide both sides by -3 which makes the -3 cancel out on the left side.

-3x / (-3) = -33 / (-3)

x = 11.

Now you can see how to solve your question Erin.

Cheers,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.