What is x = 4x + 1

Process:  get all the variables ( the x's ) to one side, and all the number terms to the other.

Since the only number term is the  1  on the right side; leave it where it is and get rid of the  4x  term from the right side by subtracting  4x  from both sides:

    x  =  4x + 1

    x - 4x  =  4x - 4x + 1            (x - 4x  becomes  -3x)

    -3x  =  1                               (divide both sides by -1)

     x  =  -1/3