Consider the equation:
-14x + P = Qx + 18
For a linear equation like this, it can have:
* one solution
* no solutions
* infinitely many solutions
For the equation to have one solution, the coefficient of the variable x must be different on each side of the equation, like in
3x + 6 = 2x - 4
For the equation to have no solutions, the coefficients of the variable x must be equal on each side and the independent term (the number alone) must be different on each side, like in the equation:
-5x + 8 = -5x +1
The above equation has no solutions
For the equation to have infinite solutions, both the coefficient and the independent term must be equal. The equation
6x - 1 = 6x - 1
has infinite solutions
Thus, for our equation to have infinite solutions:
-14x + P = Qx + 18
P = 18, and Q=-14