We provide a new event-triggered delay compensation approach for linear systems with arbitrarily long constant input delays. Our prediction map is expressible as a solution of a discrete time system. Our method ensures input-to-state stability. We also provide an analog under measurement delays, where the prediction map is expressible as a solution of a continuous-discrete system. Significant novel features are our combined use of matrices of absolute values and our prediction based event triggers, instead of Euclidean norms, and the fact that the predictor dynamics always has the same dimension as that of the original system. Our marine robotic example illustrates an advantage of using our new methods.