We search for CP-violating charge asymmetries (alpha(CP)) in the B meson decays to K(+/-)pi(-/+), K(+/-)pi(0), K(0)(S)pi(+/-), K(+/-)eta('), and omega pi(+/-). Using 9.66 million upsilon(4S) decays collected with the CLEO detector, the statistical precision on alpha(CP) is in the range of +/-0.12 to +/-0.25 depending on decay mode. While CP-violating asymmetries of up to +/-0.5 are possible within the standard model, the measured asymmetries are consistent with zero in all five decay modes studied.