  Linear vector equations and inequalities are considered defined in terms of
idempotent mathematics. To solve the equations, we apply an approach that is
based on the analysis of distances between vectors in idempotent vector spaces.
The approach reduces the solution of the equation to that of an optimization
problem in the idempotent algebra setting. Based on the approach, existence and
uniqueness conditions are established for the solution of equations, and a
general solution to both linear equations and inequalities are given. Finally,
a problem of simultaneous solution of equations and inequalities is also
considered.
