Direct way of solving modulus containing equations

[phymatter]

can someone tell me a direct way of solving modulus containing equations other than taking different cases with all terms ,
i mean if we have an equation of the kind |a|+|b|-|c|-|d|=|e|+|f| ,where a,b,c..are some expressions , i cannot take 12 cases! , there would definitely be some technique to solve it directly , please help!

 

[HallsofIvy]

Oddly enough, there are, in fact, many of us who can count to 12! Taking 12 cases is not all an impossible situation. However, here your real problem is that you have 6 different unknown numbers. What are you trying to solve for and what are the conditions on the other numbers?

 

[phymatter]

i accept that we can count to 12 ,
but here the question is to adopt a quicker approach , say if there were many more variables , then ??
well as i had said a,b,c.. are some expressions in x
as an example say it is :
|2x+3|+|4x-2|-|6x|-|5-7x|=|7x+3|+|9x+2|
(i have just cooked up the values , even i do not know the answer , but it gives the idea of what i am trying to ask)

 

[Tac-Tics]

i accept that we can count to 12 ,
but here the question is to adopt a quicker approach , say if there were many more variables , then ??
well as i had said a,b,c.. are some expressions in x
as an example say it is :
|2x+3|+|4x-2|-|6x|-|5-7x|=|7x+3|+|9x+2|
(i have just cooked up the values , even i do not know the answer , but it gives the idea of what i am trying to ask)

There is no general solution for an ambiguous problem in math. The solution will always be buried in the exact details of the problem.

Generally speaking, if the problem you are working on exhibits some kind of symmetry, terms might cancel out, and the number of cases will be reduced. Otherwise, there's no guarantees.