SOLUTION: 9(x-4)-8x=x-1 x=

9(x - 4) - 8x = x - 1

Remove the parentheses by the distributive property.
That means to multiply the 9 times both the x and the
-4.  When we multiply the 9 by the x we get 9x.
When we multiply the 9 by the -4 we get -35

9x - 36 - 8x = x - 1

Now combine the 9x with the -8x and get 1x or just x
on the left:

      x - 36 = x - 1

Now to get rid of the x on the right, we subtract x
from both sides:

      x - 36 = x - 1
     -x       -x
  ---------------------
         -36 =    -1

That is a FALSE numerical equation (no variables).

Therefore there is no solution.  This kind of 
equation is called a CONTRADICTION.  

(Note: Sometimes you end up with a TRUE numerical 
equation (no variables.  An example of that is:

5(x + 4) - 2x = 20 + 3x

Remove the parentheses by the distributive property.
That means to multiply the 5 times both the x and the
4.  When we multiply the 5 by the x we get 5x.
When we multiply the 5 by the 4 we get 20

5x + 20 - 2x = 20 + 3x

Now combine the 5x with the -2x and get 3x:

     3x + 20 = 20 + 3x

Now to get rid of the 3x on the right, we subtract 3x
from both sides:

     3x + 20 = 20 + 3x
    -3x            -3x
  ---------------------
          20 = 20

That is a TRUE numerical equation (no variables).

Therefore there are MANY solutions.  In fact,
every number in the world is a solution to it!  

This kind of equation is called an IDENTITY. 

Edwin