Evaluate (complex solution)
|X-C|+|X-G|+|X-ϕ|<1
Solve for ϕ
ϕ\in \left(|X-C|+|X-G|+X-1,-|X-C|-|X-G|+X+1\right)
\left(G<C+1\text{ and }X\geq C\text{ and }X<G\right)\text{ or }\left(X>\frac{C+G-1}{2}\text{ and }X<C\text{ and }X<G\right)\text{ or }\left(X<\frac{C+G+1}{2}\text{ and }X\geq C\text{ and }X\geq G\right)\text{ or }\left(G>C-1\text{ and }X<C\text{ and }X\geq G\right)
Solve for X
\left\{\begin{matrix}X\in [ϕ,C)\text{, }&(G\leq ϕ\text{ and }ϕ<C\text{ and }G>-(1+ϕ-2C))\text{ or }(G\geq C\text{ and }ϕ<C\text{ and }G<1+2ϕ-C)\\X\in (C+G-ϕ-1,G)\text{, }&ϕ>C-1\text{ and }G<C\text{ and }G\geq 1+2ϕ-C\\X\in (C+G-ϕ-1,C)\text{, }&G\geq C\text{ and }G\geq 1+2ϕ-C\text{ and }G<ϕ+1\\X\in [ϕ,G)\text{, }&(G>ϕ\text{ and }G<\frac{C+ϕ+1}{2}\text{ and }ϕ>C)\text{ or }(G>ϕ\text{ and }G<C\text{ and }G<1+2ϕ-C)\\X\in [ϕ,C-G+ϕ+1)\text{, }&G\geq \frac{C+ϕ+1}{2}\text{ and }G<C+1\text{ and }ϕ>C\\X\in [C,G)\text{, }&(G>C\text{ and }G<ϕ\text{ and }G<2C-ϕ+1)\text{ or }(G>C\text{ and }G<\frac{C+ϕ+1}{2}\text{ and }ϕ\leq C)\\X\in [C,C-G+ϕ+1)\text{, }&G\geq \frac{C+ϕ+1}{2}\text{ and }ϕ\leq C\text{ and }G<ϕ+1\\X\in (\frac{C+G+ϕ-1}{3},ϕ)\text{, }&G\geq ϕ\text{ and }G<1+2ϕ-C\text{ and }ϕ<C\\X\in (\frac{C+G+ϕ-1}{3},G)\text{, }&(G>\frac{C+ϕ-1}{2}\text{ and }G<ϕ\text{ and }ϕ<C)\text{ or }(G>\frac{C+ϕ-1}{2}\text{ and }G<C\text{ and }ϕ\geq C)\\X\in (\frac{C+G+ϕ-1}{3},C)\text{, }&G\geq C\text{ and }ϕ\geq C\text{ and }G<2C-ϕ+1\\X\in (-C+G+ϕ-1,ϕ)\text{, }&G\geq ϕ\text{ and }G<C+1\text{ and }G\geq 2C-ϕ+1\\X\in [C,ϕ)\text{, }&(G\leq C\text{ and }ϕ>C\text{ and }G>-C+2ϕ-1)\text{ or }(G\geq ϕ\text{ and }ϕ>C\text{ and }G<2C-ϕ+1)\\X\in (-C+G+ϕ-1,G)\text{, }&ϕ<C+1\text{ and }G<ϕ\text{ and }G\geq 2C-ϕ+1\\X\in [ϕ,1+ϕ+G-C)\text{, }&G\leq ϕ\text{ and }G>C-1\text{ and }G\leq -(1+ϕ-2C)\\X\in [G,C)\text{, }&(G<C\text{ and }G>\frac{C+ϕ-1}{2}\text{ and }ϕ\geq C)\text{ or }(G<C\text{ and }G>ϕ\text{ and }G>-(1+ϕ-2C))\\X\in [G,1+ϕ+G-C)\text{, }&ϕ>C-1\text{ and }G>ϕ\text{ and }G\leq -(1+ϕ-2C)\\X\in [ϕ,\frac{C+G+ϕ+1}{3})\text{, }&G\leq ϕ\text{ and }G>-C+2ϕ-1\text{ and }ϕ>C\\X\in [G,\frac{C+G+ϕ+1}{3})\text{, }&(G<\frac{C+ϕ+1}{2}\text{ and }G>ϕ\text{ and }ϕ>C)\text{ or }(G<\frac{C+ϕ+1}{2}\text{ and }G>C\text{ and }ϕ\leq C)\\X\in [C,\frac{C+G+ϕ+1}{3})\text{, }&G\leq C\text{ and }ϕ\leq C\text{ and }G>2C-ϕ-1\\X\in (C-G+ϕ-1,ϕ)\text{, }&G\leq \frac{C+ϕ-1}{2}\text{ and }G>C-1\text{ and }ϕ<C\\X\in (C-G+ϕ-1,C)\text{, }&G\leq \frac{C+ϕ-1}{2}\text{ and }ϕ\geq C\text{ and }G>ϕ-1\\X\in [G,ϕ)\text{, }&(G<ϕ\text{ and }G>C\text{ and }G>-C+2ϕ-1)\text{ or }(G<ϕ\text{ and }G>\frac{C+ϕ-1}{2}\text{ and }ϕ<C)\\X\in [G,C+G-ϕ+1)\text{, }&ϕ<C+1\text{ and }G>C\text{ and }G\leq -(C-2ϕ+1)\\X\in [C,C+G-ϕ+1)\text{, }&G\leq C\text{ and }G\leq -(C-2ϕ+1)\text{ and }G>ϕ-1\end{matrix}\right.
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