Expert Answers
pohnpei397 eNotes educator| Certified Educator

In a way, this is sort of a trick question for a couple of reasons.

First, if you just think about it, how can a number (3x) be equal to itself minus something else?  It's just not possible.

Second, if you work this out algebraically it still doesn't make any sense.  What you'd usually do here is to get all the x terms on one side and all the numbers on the other, right?  So you subtract 3x from both sides and you end up with

0-7 = 0

However, there is an answer: in algebra, when a given equation has no solution it is referred to as an empty set and you indicate that by a 0 with a diagonal line through it.


neela | Student


We shall prove that it is not an equation and when simplified it is an absurdity.So, before explaining the logical postion, we treat it as an equation and try to solve it as if it is an equation:

Subtract 3x from both sides of (1), Then,


Add 7 to both sides.

3x-3x= 7 or

0=7, which is absurd. So the 3x-7 = 3x is not an equation.

If you further analyse, you can see that in mathematics there are some thing against doing.  3x-3x=7 implies x*(3-3)=7. Or x*0=7. There are no number you get when you multiply by zero. So x is a no number.Therefore thre is no solution.

Secondly, 3x=3x is an identity true for all x. The identity or the equation of identity gets tilted and spoiled if you add or subtract something other than zero to only one side.