The examples in this subsection have been used for testing purposes by Richard Lang.

Solve the following equations ...

No.1 (17*x - 51)/9 - (-(13*x - 3)/6) + 11 - (9*x - 7)/4 = 0

... not difficult (actually a linear equation), but a lot of work.
No.2 (3*x + 5)/18 - x/2 = -((3*x - 2)/9)

Simplifying the left-side and the right-side separately shows, that this exation has no solution.
No.3 -2/x + 3/(2*x) - 4/(3*x) + 5/(4*x) + 6/(5*x) = 65/8

...again, this turns out to be a linear equation, and the following as well ...
No.4 (x + 3)/(2*x - 4) = 3
No.5 (1/2 + (5*x)/2)^2 - ((13*x)/2 - 5/2)^2 = -1*(6*x)^2 + 29
No.6 (5*x)/(x - 2) - x/(x + 2) = 4
No.7 x/(x^2 - 6*x + 9) - 1/(x^2 - 3*x) =1/x
No.8 ((x - 1)/(x + 1) + 1) / ((x - 1)/(x + 1) - (x + 1)/(x - 1)) = 2

Of course, not only x may be the identifier of the bound variable. Actually, the following equation-solving is indispensible for applied mathematics.

No.9 1/R = 1/R1+1/R2 ,  R1 = ?

This equation is well-known in electro-engineering, for instance.
No.10 m1 * v1+ m2 * v2 = 0 ,   m1 = ?
No.11 f = ((w + u) / (w + v)) * v0 ,  v = ?
No.12 f = ((w + u) / (w + v)) * v0 ,  w = ?

... often there is more than one variable to be made explicit.
No.13 y^2 = 2*p*x ,  p = ?
No.14 A = 1/2 * (x1*(y2 - y3) + x2*(y3 - y1) + x3*(y1 - y2)) ,  x2 = ?

The final equation is not given a method. ISACs problem-handler searches the hierarchy of types of equations for the most appropriate type ('automated refinement of problems') and then assigns the method(s) for solving.

No.15 (x - 4)/(x + 4) = (1 - x)/(1+ x)

This equation is not linear anymore.