Wednesday

August 20, 2014

August 20, 2014

Posted by **jasmine20** on Wednesday, January 3, 2007 at 8:38pm.

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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