Yes, synovial joints are indeed moveable.
Synovial Joints and Mobility
Synovial joints, also known as diarthroses, are the most common type of joint in the human body. The term "diarthroses" itself means they are freely mobile. This high degree of mobility distinguishes them from fibrous and cartilaginous joints. A key structural characteristic specific to synovial joints is the presence of a joint cavity, contributing to their mobility.