  First-order predicate logic extended with linear arithmetic is undecidable,
in general. We show that the Bernays-Sch\"onfinkel-Ramsey (BSR) fragment
extended with linear arithmetic restricted to simple bounds (SB) is decidable
through finite ground instantiation. The identified ground instances can be
employed to restrict the search space of existing automated reasoning
procedures for BSR(SB). Satisfiability of BSR(SB) compared to BSR remains
NEXPTIME-complete. The decidability result is almost tight because BSR is
undecidable if extended with linear difference inequations, simple additive
inequations, quotient inequations and multiplicative inequations.
