Using data collected with the HyperCP (E871) spectrometer during the 1997 fixed-target run at Fermilab, we report the first observation of the decay K--->pi(-)mu(+)mu(-) and new measurements of the branching ratios for K+/--->pi(+/-)mu(+)mu(-). By combining the branching ratios for the decays K+-->pi(+)mu(+)mu(-) and K--->pi(-)mu(+)mu(-), we measure Gamma(K+/--->pi(+/-)mu(+)mu(-))/Gamma(K+/--->all) = (9.8+/-1.0+/-0.5)x10(-8). The CP asymmetry between the rates of the two decay modes is [Gamma(K+-->pi(+)mu(+)mu(-))-Gamma(K--->pi(-)mu(+)mu(-))]/[Gamma(K+-->pi(+)mu(+)mu(-))+Gamma(K--->pi(-)mu(+)mu(-))] = -0.02+/-0.11+/-0.04.