Expert: Josh - 4/11/2006

Question
I really am stuck and can not get a hold of my professor so here goes

the problem is x/6+3/4=x-1/4  I have found the lcd whic is 12 so I have 12*x/6+12*3/4=12*x-1/4 from here I am lost.  Could you please help?

Answer
It's better to use parenthesis when writing fractions on a single line. From 12*x/6+12*3/4=12*(x-1)/4, you cancel out the common factors to turn this expression into an equation (with no fractions in it).

e.g., 12/6=2, (12*3)/4=36/4=9, 12/4=3, so we have
2x+9=3(x-1) from the previous line.

Now, expand the right hand side (RHS) of the equation to
2x+9=3x-3

Then, you isolate the knowns from the unknown,
2x-3x=-3-9
-x=-12
Therefore, the solution is x=12.

Check that this is correct by back-substitution.
Putting x=12 into  x/6+3/4=(x-1)/4 gives 12/6+3/4=11/4. Is this true? Well, the left hand side (LHS) = (24/12)+(9/12)=33/12=11/4 = RHS.

So, we haven't made any mistake.