Question

Create your own two-step equation with NO SOLUTION as the solution. Show the steps to solving the equation and explain in words why your work proves that there are NO SOLUTIONS.

Answer 1

"Create your own two-step equation with NO SOLUTION as the solution. Show the steps to solving the equation and explain in words why your work proves that there are NO SOLUTIONS. "

By the phrase "NO SOLUTION" do you mean "NO UNIQUE SOLUTION"? or "NO POSSIBLE SOLUTION"? (and yes there is a difference!)

If you meant "NO POSSIBLE SOLUTION", then how about this one:

3x – x = x + x + 3

Solving ...

step ➊: Collect like terms ➞ 2x = 2x +3

step ➋: Subtract 2x from both sides ➞ 0 = 3

This of course is a untrue conclusion, which implies the original equation has no possible solution; there is NO number that will ever make this equation true.



If you meant "NO UNIQUE SOLUTION", then how about this one:

3x – x = x + x

Solving ...

step ➊: Collect like terms ➞ 2x = 2x

step ➋: Subtract 2x from both sides ➞ 0 = 0

This is a "true" conclusion, .... but .... what happened to "x"?

This implies the original equation has no UNIQUE solution; that is to say, EVERY number that you can think of will make this equation true.

This is a special kind of equation called an IDENTITY.


Source: http://answers.yahoo.com/question/index?qid=20101101090101AAEtJNL