Jalil and Victoria are each asked to solve the equation ax – c = bx + d for x. Jalil says it is not possible to isolate x because each x has a different unknown coefficient. Victoria believes there is a solution, and shows Jalil her work:

Accepted Solution

solve the equation ax – c = bx + d for x:

1) Group the x terms together on the left:     ax - bx - c = d

2) Group the constant terms together:          ax - bx = c + d

3) factor out x:                                             x(a - b) = c + d

4) Divide both sides of the equation by (a - b) to obtain a formula for x:
           x(a - b) = c + d   =>    x = ---------

This shows that the given equation CAN be solved for x, but there is a restriction:  a must NOT equal b, because if a-b = 0, we'd have division by zero (which is not defined).

Where is Victoria's solution?  Please share it if you want to discuss this problem further.  Thank you.