Dexterous manipulation learning has long been hindered by the high costs of data and training, as pure reinforcement learning typically requires large-scale interactive exploration and imitation learning depends on high-quality demonstrations that are expensive to collect. To address this problem, we propose EaDex, a multi-embodiment dexterous manipulation learning framework under low-cost demonstration conditions, which enables rapid generation of demonstration data and consequently reduces training time for efficient dexterous manipulation. At the data level, EaDex captures human hand motions using only a single RGB-D camera and constructs structured demonstration data through MANO-based hand modeling, data normalization, and motion retargeting. At the learning level, we introduce a contact-reward-based dynamic demonstration annealing mechanism, which guides early-stage exploration under demonstration and gradually transitions to autonomous optimization with accumulating contact rewards. Using our custom dataset, we evaluate EaDex on three dexterous hands and three articulated object-opening tasks, covering nine cross-embodiment manipulation settings, achieving a 55.3% relative improvement over the baseline without demonstration annealing. These results validate the effectiveness of the proposed low-cost demonstration pipeline and the dynamic demonstration annealing strategy for dexterous manipulation learning.