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

this is 2

Of course, I'm here to help! I understand that the concept of solutions in equations can sometimes be confusing, so I'll try my best to explain it clearly.

In mathematics, a solution to an equation is a value or values that make the equation true. When we say an equation has no solution, it means that there is no value we can substitute for the variable that will satisfy the equation, making it true. In other words, the equation is not possible to solve.

In the equation 3x = 3x + 5, no matter what value we choose for x, the equation will never be true. If we simplify it, we get 0 = 5, which is clearly false. Therefore, there are no values of x that can make this equation true, and it has no solution.

On the other hand, in the equation 7x + 8 = 8, if we substitute x = 0, the equation becomes 7(0) + 8 = 8, which simplifies to 8 = 8. Here, the equation is true, and we have found a value (x = 0) that satisfies it. So, the solution to this equation is x = 0.

The difference between a solution of zero and no solution lies in the existence of at least one value that satisfies the equation. If an equation has no solution, it means there is no value that makes the equation true. However, if an equation has a solution of zero, it means that substituting zero for the variable satisfies the equation.

I hope this explanation clarifies the difference between a solution of zero and no solution. If you have any further questions, feel free to ask!

You're welcome! I'm glad I could help clarify the difference between having no solution and having zero as a solution. If you have any more questions, feel free to ask!