I am using Wolfram Alpha, and I have four equations and inequalities. They are nested, i.e., I can make one very long expression out of the four. I want the long expression to be solved for one of its variables. If I enter the equations/inequalities separately, this works up to two equations, but with three or more, Wolfram Alpha does not understand anymore the input. The very long expresison which I get if I put together everything is also not understood. Concretely, these are my four expressions

(1) p*O_1+(1-p)*((1/2)*D_1+delta) >= p*(1/2)*D_2+(1-p)*(1/2)*D_1

(2) O_1 = ((a_1/(a_1+a_2))*D_1+(c_1*a_2)/(a_1+a_2)-(c_2*a_1)/(a_1+a_2))

(3) c_1 = ((1/2)*D_1 - (a_1/(a_1+a_2))*D_2)

(4) c_2 = ((1/2)*D_1 - (a_2/(a_1+a_2))*D_2)

and this is my consolidated inequality

p*((a_1/(a_1+a_2))*D_1+(((1/2)*D_1 - (a_1/(a_1+a_2))*D_2)*a_2)/(a_1+a_2)-( ((1/2)*D_1 - (a_2/(a_1+a_2))*D_2)*a_1)/(a_1+a_2))+(1-p)*((1/2)*D_1+delta) >= p*(1/2)*D_2+(1-p)*(1/2)*D_1

I want to solve the consolidated inequality for p, i.e., p should be alone on one side of the inequality sign.

Any ideas why Wolfram Alpha understands each of the parts (1)-(4), and even two of them together, but not the long expression and also does not understand if I enter more than two of the individual equations/inequalities? Any tricks how I can make this work and circumvent potential Wolfram Alpha input length limitations?