CountIblis, can i bother you

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Countiblis, i know that you might be busy do you mind if i ask you the following for help.Only if you can please.

can you explain to me just one more thing so i can undestand it.

Now i have an equation which is :
3x = 3x + 5
which I know has no solution to it,
now whereas the equation 7x + 8 = 8 has zero as a solution.

What is the difference between a solution of zero and no solution?

If an equation has no solution then that means that no value for x will satisfy the equation. So, the equation

3x = 3x + 5

has no solutions.

Note that the value x = 0 is then also not a solution.

The equation

7x + 8 = 8

Does have a solution: x = 0. So, this is clearly a different situation than no solutions at all.

If you have no solutions then the number of solutions is zero. If you have one solution, say, x = 0, then the number of solutions is 1.

So, to confuse the two cases amounts to confusing the size of the set of all solutions with the solutions themselves.

I appreciate your help

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