Suppose that \(A_k(z),...,A_0(z)\) are analytic functions without common zeros on the complex plane \(C\) and the indecomposable equation \[ A_k(z)W^k+A_{k-1}(z)W^{k-1}+\cdots+A_0(z)=0 \tag{1} \] defines a \(k\)-valued algebroidal function \(W(z)\) on the complex plane. There are lots of difficulties on the research of the algebroidal functions, and many important theorems on meromorphic function can not be extended to algebroidal functions for its multivaluedness and the complexity of its branch points. The author uses a basic inequality [see \textit{Z.-S. Gao} and the author, J. Math. Anal. Appl. 325, No. 1, 268--278 (2007; Zbl 1142.30329)] to prove that a \(k\)-valued algebroidal function \(W(z)\) defined by (1) has a \(T\)-direction dealing with multiple values \(l(\geq 2v+1)\) of \(W(z)\), provided it satisfies \[ \overline{\lim_{r\rightarrow\infty}} \frac{T(r,w)}{\log^2 r}=+\infty; \quad\text{ or }\quad \overline{\lim_{r\rightarrow\infty}} \frac{T(2r,w)}{T(r,w)}>1. \] This is a problem from \textit{J. H. Zheng} (see Problem 5.12 of [\textit{J. H. Zheng}, On value distribution of meromorphic functions with respect to arguments, preprint]).