No solution? Undefined? All real numbers? Peice of cake.

A) Create and solve an equation that has no solution. B) Explain (clearly) when an equations has no solution

This was a question from the Equations and Inequalities POK I took on October 8th, back when I had a hazy understanding of "No Solution", "All Real Numbers", and "Undefined".

My mistake in the above problems was that I confused the definitions of "No Solution" and "All Real Numbers" in my creation of a "No Solution" problem and my definition of an equation with no solution was inaccurate and ambiguous.

Well, after some clarifications with my teacher and my notes I can now say I know what each of those terms mean. Here are my corrections.

NO SOLUTION: When the solution obtained is not true and no value of 'x' will satisfy the equation.
Example:
2+7x=6+7x
  -7x      -7x
     2=6
2 does not  equal 6 so the equations has no solution.

UNDEFINED: When the solution has zero in the denominator.

ALL REAL NUMBERS: When any and all real numbers substituted in for 'x' will satisfy the equation.
Example:
6+9x=6+3(3x)
6+9x=6+9x
-6     -6
    9x=9x
This sentence is true therefore it will be true for all real values of 'x'.

I threw in some extra definitions, just so the differences between them would be clear. Ahh the joy of learning.