SOLUTION: 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 betwe

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Question 65939: 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?
Found 2 solutions by 303795, stanbon:
Answer by 303795(602) (Show Source):
You can put this solution on YOUR website!
No solution implies that it is not possible to find any number which will make the equation true. There is no solution. In your example whatever number you test as x the right hand side of your equation will be 5 more than the value on the left hand side. They can never be equal!
3x = 3x + 5

The solution of x=0 implies that there actually is a solution. In your quoted example if x=0 then the equation is true. 8 does equal 8. If x is any other value the equation is not true. When x is a negative number the left hand side is less than the right hand side. When x is a positive number the left hand side is greater than the right hand side. The two sides are equal only when x=0.
7x + 8 = 8

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Zero is a solution because it is a Real number that
generates a true statement when it replaces "x".
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3x=3x+5 is an equation based on the assumption
the "x" on the left is the same NUMBER as the
"x" on the right.
But if you subtract 3x from both sides you get
0=5. That is a contradiction which results from
the origial assumption.
So, the assumption is incorrect; there is no
number value that "x" can have.
Cheers,
Stan H.