Question

Felix wrote several equations and determined that only one of the equations has no solution. Which of these equations has no solution?

Answer 1

3(x-2)+x=4x+6

Explanation:

The first equation is the one that doesn't have solution. Let's demonstrate this:

`3(x-2)+x=4x+6\\3x-6+x=4x+6\\4x-6=4x+6\\4x-4x=6+6\\0=12`

As you can observe, the equation doesn't have any solutions, because it result in a false statement.

If we solve the other equations, we would have:

`3(x-2)+x=2x-6\\3x-6+x=2x-6\\4x-6=2x-6\\4x-2x=-6+6\\2x=0\\x=0`

`3(x-2)+x=3x-3\\3x-6+x=3x-3\\4x-3x=-3+6\\x=3`

`3(x-2)+x=4x-6\\3x-6+x=4x-6\\4x-6=4x+6\\6=6`

The last equation has infinite solutions.

Therefore, the only one that doesn't have any solutions is

3(x-2)+x=4x+6

Answer 2

3(x-2)+x=4x+6

Explanation:

case 1) we have

3(x-2)+x=4x-6

Solve for x

3x-6+x=4x-6

4x-6=4x-6

0=0 ----> is true for any value of x

therefore

The equation has infinite solutions

case 2) we have

3(x-2)+x=2x-6

3x-6+x=2x-6

4x-2x=-6+6

2x=0

x=0

case 3) we have

3(x-2)+x=3x-3

3x-6+x=3x-3

4x-3x=-3+6

x=3

case 4) we have

3(x-2)+x=4x+6

3x-6+x=4x+6

4x-4x=6+6

0=12 ------> is not true

therefore

The equation has no solution