SOLUTION: Solve the following equation by clearing denominators and decimals first: -2.3-4.2r=37.58

Solve the following equation by clearing denominators 
and decimals first: 

-2.3 - 4.2r = 37.58

Look at the number of digits after the three decimals:

-2.3 has one digit after the decimal
-4.2 has one digit after the decimal
37.58 has two digits after the decimal

The most number of digits after the decimal is two.

Therefore we must move all three of the decimals two
places to the right in order to get them to become
whole numbers.  This is the same as multiplying
through by 100.

 -2.3 with the decimal moved two places right is -230.
 -4.2 with the decimal moved two places right is -420.
37.58 with the decimal moved two places right is 3758.

So the original equation

   -2.3 - 4.2r = 37.58

becomes

   -230 - 420r = 3758

add 230 to both sides:

   -230 - 420r = 3758
   +230          +230
  --------------------
         -420r = 3988

Divide both sides by -420

       -420r     3988
      ------- = ------
       -420      -420

The fraction on the right side reduces 
by dividing numerator and denominator by 4.
It is a negative fraction because the
numerator is positive and the denominator
is negative and a positive divided by a 
negative is negative:

            r = -997/105

or you can divide out the fraction and
get this decimal

            r = -9.495238095  

Now since the smallest number of decimals
places in the original equation was 1, 
round the final answer off the same way, so

            r = -9.5

Edwin