The present disclosure provides substituted pyridyl-, pyrimidinyl-, pyrazinyl-,pyridazinyl-, and triazinyl-based carboxamides of Formula I-A:and the pharmaceutically acceptable salts and solvates thereof, wherein Z,HET, R10, and Eare defined as set forth in the specification. The present disclosure is alsodirected to the useof compounds of Formula I-A to treat a disorder responsive to the blockade ofsodiumchannels. Compounds of the present disclosure are especially useful fortreating pain.