I suspect you read that actual floating point optimization solvers treat strict inequalities ($<$ and $>$) as non-strict inequalities ($\le$ and $\ge$). Solvers also give themselves a fudge factor, called feasibility tolerance, equal to the amount by which they may be violated in reality but treated as satisfying the constraint by the solver. If you must really have strict inequality and strict feasibility for a $\le$ constraint, $\textsf{LHS} < \textsf{RHS}$, then pick a number "margin", such that
$$\textsf{margin > feasibility tolerance}$$
and make your constraint
$$\sf LHS + margin \le RHS.$$
Similarly for $>$.
Equality constraints are treated by solvers as being satisfied if they are violated by no more than the feasibility tolerance. If you can not choose a feasibility tolerance which satisfies your desires across all constraint types to which it applies, then you can instead use two inequality constraints, with whatever tolerance for "equality satisfaction" you want. So, for the equality constraint $\sf LHS = RHS$, you could treat it as being $\sf |LHS - RHS| \le tolerance$, which is equivalent to
$$\sf LHS - RHS \le tolerance,\quad\sf RHS - LHS \le tolerance$$
Keep in mind, that solvers will treat $\sf LHS = RHS$ as being $\sf |LHS - RHS| \le \textsf{feasibility tolerance}$.
You will never get (ensure) equality constraints satisfied strictly in floating point solvers.