Question

Why doens't `2+2x=3+2x` have a solution?

Answer 1

You get a contradiction.

Explanation:

Look at the original equation:

`2x+2=2x+3`

Subtracting `2x` from both sides:

`cancel(2x)+2-cancel(2x)=cancel(2x)+3-cancel(2x)`

`2=3`

But we know that `2!=3`, because no natural number can be equal to another one!

So, we can conclude that `x` does not have a solution.

Answer 2

Because we ended up having `0=1`

Explanation:

`2+2x =3+2x`

let's start by subtracting `2x` from both sides

`2+2x - 2x = 3 + 2x - 2x`

`2= 3`

Then we subtract `2` from both sides

`2-2=3-2`

`0=1`

Thus,

There are no solutions!