A simple accurate lower bound for all the bound-state systems; for the first-order gradient correction to the exchange-energy functional, viz., K1(2)[rho] = beta integral[del rho(r)(2)/(rho(4/3)(r))] dr greater than or equal to 27(pi/2)(4/3) beta[rho(r)](1/3) = 0.27 1[rho](1/3) has been derived where [rho(r)] is the average electron density. The result is numerically analyzed. An empirical relationship between K-2[rho] and [rho] for neutral atoms has also been proposed.