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

any ideas yet

Answer 2

Start with a contradiction, for example 0=1. Now you can do a lot, for example add x to both sides:
x=x+1
and another step, for example divide by 2:
x/2 = (x+1)/2

This is our equation, if we do the steps backward (multiply by 2, subtract x), we get to our contradiction.

Answer 3

u sure

Answer 4

Yeah.

Answer 5

If you don't believe me, just try to find a x that satisfies x/2 = (x+1)/2
;)

Answer 6

lol i believe you. i dont feel like doing work by myself. :)

Answer 7

You could also argue that they are the two lines
y=x/2
y=(x+1)/2=x/2+1/2,
which are parallell. Since two lines never meet there are no solutions.

Answer 8

would that be anothre example or the same one

Answer 9

and thanks for helping me :)

Answer 10

That's the same example.
If you really wanna show off you could do something like
\[ \frac{1}{x+5} = 0 \]
and say that's it's asymptotic to the x-axis. Then you could argue that it has solutions +∞ and -∞ if you extend the reals to include surreal numbers and be the coolest kid in class.

Answer 11

lol 1) i dont know what asymptotic means and 2) i dont think that will make me be the coolest kid in my class

Answer 12

You must have very lame classmates, everybody knows math is awesome =)

Answer 13

yeah but i dont take math at school i take online, but my classmates in my other classes might be lame. idk i feel like they are