 
When we are first introduced to equations, the equation format we are taught is closed equation format, that is y = f(x).
For example,
 y = mx + c   equation of a straight line 
 Q = UALmtd   design equation of heat exchanger 
To write an equation in open equation format, the closed format equation is rearranged with all the terms on one side. The equation is then evaluated to find the residual. For example;
 Closed Equation Format   Open Equation Format 
 y = mx + c   R = y  mx  c 
 Q = UALmtd   R = Q  UALmtd 
So why would we want to work with open equations?
 For linear equations, any term in the equation, (not just the lefthand term), can be found without the need rearrange the equation or solve it via iteration,
 If the model is overspecified the use of open equations provides a method to reconcile the data,
 Interrelated equations can be linked by simple connection equations can be used, rather than eliminating variables and equations
