#### Question

# Two-step equation with no solutions example?

I need two-step equation that doesn't have no solution. I tried to make a problem that doesn't have a solution, but my teacher said it did =( So now I'm stuck and I don't know how to make one.

#### Answer

A problem that has no solution is one where the last line is clearly false.

3(2x + 5) = 2(3x + 4)

6x + 15 = 6x + 8

15 = 8 --> clearly false

2x + 17 = 3x - 6 - x

2x + 17 = 2x - 6

17 = -6 --> clearly false

On the other hand, a problem whose last line is clearly true has an infinite number of solutions(all real numbers). Any and every value chosen for x will 'work.'

3(2x + 8) = 2(3x + 12)

6x + 24 = 6x + 24

24 = 24 --> clearly true

x + 17 = 2x - (x - 5) + 12

x + 17 = 2x - x + 5 + 12

x + 17 = x + 17

17 = 17 --> clearly true

You mean like this:

x^2 + 1000 = - 1000

or x^1/2 + 10 = - 24 ?

This isn't that clear haha. There is many problems that aren't solvable like 1 < 0, I'm guessing that isn't what you are looking for though.

9+4x-7=8x+5-4x

9-7+4x=8x-4x+9

2+4x=4x+9

- 4x -4x

2=9

just make up any problem that has the 2 x's cancel out

for example

2x+1=2x+7