Sample Problem

3x – 7  =  9 – 5x

Think of the = sign as a brick wall.

“x”            “#”
3x – 7  =  9 – 5x

One side of the brick wall is the x’s side, and the other side is the number’s side.

3x – 7  =  9 – 5x
+ 7   + 7
3x        = 16 – 5x

Now we look for “trespassers”!  Is anybody on the wrong side?  Starting from the left, we come to the 3x.  3x is on the x’s side so that’s ok.  Next we come to the –7, which should not be on the x’s side.  How do we remove it?  We think of “opposites”.  The opposite of –7 is +7.  Whatever we do to one side of the brick wall, we must do to the other side.  So we do a +7 on both sides.

3x       = 16 – 5x

The trespassing –7 has been successfully removed, and now our equation looks like this.

3x      = 16 – 5x
+5x             + 5x
8x       = 16

We continue looking for trespassers.  The 16 is ok on the numbers side, but that –5x must go!  Again we do “opposites”, so we see a +5x on both sides.

8x   =   16

That trespassing +5x has been removed, and now our equation looks like this.  We have completed our mission!  We now have all of the x’s on one side of the brick wall, and all of the numbers on the other side.

8x     =  16
8            8

The last step is to divide both sides by that last number in front of the x.

x = 2

And we have our final answer!