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We solve stabilization problems of LTI systems with unknown parameters and distributed input delay. The key challenge is that the infinite-dimensional input dynamics are distributed, which makes traditional infinite-dimensional backstepping inapplicable. We resolve this challenge by employing backstepping-forwarding transformations of the finite-dimensional state of the plant and of the infinite-dimensional actuator state, which enable us to design Lyapunov-based update laws. Using the estimations of the unknown parameters, the certainty equivalent linear state feedback results in a nonlinear adaptive control law. We illustrate our design with a simulation example.