code: def solve_univariate_inequality(
      expr, gen, relational=True, domain=S.Reals, continuous=False
  ):
      """Solves a real univariate inequality.
  
      Parameters
      ==========
  
      expr : Relational
          The target inequality
      gen : Symbol
          The variable for which the inequality is solved
      relational : bool
          A Relational type output is expected or not
      domain : Set
          The domain over which the equation is solved
      continuous: bool
          True if expr is known to be continuous over the given domain
          (and so continuous_domain() does not need to be called on it)
  
      Raises
      ======
  
      NotImplementedError
          The solution of the inequality cannot be determined due to limitation
          in :func:`sympy.solvers.solveset.solvify`.
  
      Notes
      =====
  
      Currently, we cannot solve all the inequalities due to limitations in
      :func:`sympy.solvers.solveset.solvify`. Also, the solution returned for trigonometric inequalities
      are restricted in its periodic interval.
  
      See Also
      ========
  
      sympy.solvers.solveset.solvify: solver returning solveset solutions with solve's output API
  
      Examples
      ========
  
      >>> from sympy import solve_univariate_inequality, Symbol, sin, Interval, S
      >>> x = Symbol('x')
  
      >>> solve_univariate_inequality(x**2 >= 4, x)
      ((2 <= x) & (x < oo)) | ((-oo < x) & (x <= -2))
  
      >>> solve_univariate_inequality(x**2 >= 4, x, relational=False)
      Union(Interval(-oo, -2), Interval(2, oo))
  
      >>> domain = Interval(0, S.Infinity)
      >>> solve_univariate_inequality(x**2 >= 4, x, False, domain)
      Interval(2, oo)
  
      >>> solve_univariate_inequality(sin(x) > 0, x, relational=False)
      Interval.open(0, pi)
  
      """
      from sympy.solvers.solvers import denoms
  
      if domain.is_subset(S.Reals) is False:
          raise NotImplementedError(
              filldedent(
                  """
          Inequalities in the complex domain are
          not supported. Try the real domain by
          setting domain=S.Reals"""
              )
          )
      elif domain is not S.Reals:
          rv = solve_univariate_inequality(
              expr, gen, relational=False, continuous=continuous
          ).intersection(domain)
          if relational:
              rv = rv.as_relational(gen)
          return rv
      else:
          pass  # continue with attempt to solve in Real domain
  
      # This keeps the function independent of the assumptions about `gen`.
      # `solveset` makes sure this function is called only when the domain is
      # real.
      _gen = gen
      _domain = domain
      if gen.is_extended_real is False:
          rv = S.EmptySet
          return rv if not relational else rv.as_relational(_gen)
      elif gen.is_extended_real is None:
          gen = Dummy("gen", extended_real=True)
          try:
              expr = expr.xreplace({_gen: gen})
          except TypeError:
              raise TypeError(
                  filldedent(
                      """
                  When gen is real, the relational has a complex part
                  which leads to an invalid comparison like I < 0.
                  """
                  )
              )
  
      rv = None
  
      if expr is S.true:
          rv = domain
  
      elif expr is S.false:
          rv = S.EmptySet
  
      else:
          e = expr.lhs - expr.rhs
          period = periodicity(e, gen)
          if period == S.Zero:
              e = expand_mul(e)
              const = expr.func(e, 0)
              if const is S.true:
                  rv = domain
              elif const is S.false:
                  rv = S.EmptySet
          elif period is not None:
              frange = function_range(e, gen, domain)
  
              rel = expr.rel_op
              if rel in ("<", "<="):
                  if expr.func(frange.sup, 0):
                      rv = domain
                  elif not expr.func(frange.inf, 0):
                      rv = S.EmptySet
  
              elif rel in (">", ">="):
                  if expr.func(frange.inf, 0):
                      rv = domain
                  elif not expr.func(frange.sup, 0):
                      rv = S.EmptySet
  
              inf, sup = domain.inf, domain.sup
              if sup - inf is S.Infinity:
                  domain = Interval(0, period, False, True).intersect(
                      _domain
                  )
                  _domain = domain
  
          if rv is None:
              n, d = e.as_numer_denom()
              try:
                  if (
                      gen not in n.free_symbols
                      and len(e.free_symbols) > 1
                  ):
                      raise ValueError
                  # this might raise ValueError on its own
                  # or it might give None...
                  solns = solvify(e, gen, domain)
                  if solns is None:
                      # in which case we raise ValueError
                      raise ValueError
              except (ValueError, NotImplementedError):
                  # replace gen with generic x since it's
                  # univariate anyway
                  raise NotImplementedError(
                      filldedent(
                          """
                      The inequality, %s, cannot be solved using
                      solve_univariate_inequality.
                      """
                          % expr.subs(gen, Symbol("x"))
                      )
                  )
  
              expanded_e = expand_mul(e)
  
              def valid(x):
                  # this is used to see if gen=x satisfies the
                  # relational by substituting it into the
                  # expanded form and testing against 0, e.g.
                  # if expr = x*(x + 1) < 2 then e = x*(x + 1) - 2
                  # and expanded_e = x**2 + x - 2; the test is
                  # whether a given value of x satisfies
                  # x**2 + x - 2 < 0
                  #
                  # expanded_e, expr and gen used from enclosing scope
                  v = expanded_e.subs(gen, expand_mul(x))
                  try:
                      r = expr.func(v, 0)
                  except TypeError:
                      r = S.false
                  if r in (S.true, S.false):
                      return r
                  if v.is_extended_real is False:
                      return S.false
                  else:
                      v = v.n(2)
                      if v.is_comparable:
                          return expr.func(v, 0)
                      # not comparable or couldn't be evaluated
                      raise NotImplementedError(
                          "relationship did not evaluate: %s" % r
                      )
  
              singularities = []
              for d in denoms(expr, gen):
                  singularities.extend(solvify(d, gen, domain))
              if not continuous:
                  domain = continuous_domain(expanded_e, gen, domain)
  
              include_x = "=" in expr.rel_op and expr.rel_op != "!="
  
              try:
                  discontinuities = set(
                      domain.boundary
                      - FiniteSet(domain.inf, domain.sup)
                  )
                  # remove points that are not between inf and sup of domain
                  critical_points = FiniteSet(
                      *(solns + singularities + list(discontinuities))
                  ).intersection(
                      Interval(
                          domain.inf,
                          domain.sup,
                          domain.inf not in domain,
                          domain.sup not in domain,
                      )
                  )
                  if all(r.is_number for r in critical_points):
                      reals = _nsort(critical_points, separated=True)[0]
                  else:
                      sifted = sift(
                          critical_points, lambda x: x.is_extended_real
                      )
                      if sifted[None]:
                          # there were some roots that weren't known
                          # to be real
                          raise NotImplementedError
                      try:
                          reals = sifted[True]
                          if len(reals) > 1:
                              reals = sorted(reals)
                      except TypeError:
                          raise NotImplementedError
              except NotImplementedError:
                  raise NotImplementedError(
                      "sorting of these roots is not supported"
                  )
  
              # If expr contains imaginary coefficients, only take real
              # values of x for which the imaginary part is 0
              make_real = S.Reals
              if (
                  coeffI := expanded_e.coeff(S.ImaginaryUnit)
              ) != S.Zero:
                  check = True
                  im_sol = FiniteSet()
                  try:
                      a = solveset(coeffI, gen, domain)
                      if not isinstance(a, Interval):
                          for z in a:
                              if (
                                  z not in singularities
                                  and valid(z)
                                  and z.is_extended_real
                              ):
                                  im_sol += FiniteSet(z)
                      else:
                          start, end = a.inf, a.sup
                          for z in _nsort(
                              critical_points + FiniteSet(end)
                          ):
                              valid_start = valid(start)
                              if start != end:
                                  valid_z = valid(z)
                                  pt = _pt(start, z)
                                  if (
                                      pt not in singularities
                                      and pt.is_extended_real
                                      and valid(pt)
                                  ):
                                      if valid_start and valid_z:
                                          im_sol += Interval(start, z)
                                      elif valid_start:
                                          im_sol += Interval.Ropen(
                                              start, z
                                          )
                                      elif valid_z:
                                          im_sol += Interval.Lopen(
                                              start, z
                                          )
                                      else:
                                          im_sol += Interval.open(
                                              start, z
                                          )
                              start = z
                          for s in singularities:
                              im_sol -= FiniteSet(s)
                  except TypeError:
                      im_sol = S.Reals
                      check = False
  
                  if im_sol is S.EmptySet:
                      raise ValueError(
                          filldedent(
                              """
                          %s contains imaginary parts which cannot be
                          made 0 for any value of %s satisfying the
                          inequality, leading to relations like I < 0.
                          """
                              % (expr.subs(gen, _gen), _gen)
                          )
                      )
  
                  make_real = make_real.intersect(im_sol)
  
              sol_sets = [S.EmptySet]
  
              start = domain.inf
              if start in domain and valid(start) and start.is_finite:
                  sol_sets.append(FiniteSet(start))
  
              for x in reals:
                  end = x
  
                  if valid(_pt(start, end)):
                      sol_sets.append(Interval(start, end, True, True))
  
                  if x in singularities:
                      singularities.remove(x)
                  else:
                      if x in discontinuities:
                          discontinuities.remove(x)
                          _valid = valid(x)
                      else:  # it's a solution
                          _valid = include_x
                      if _valid:
                          sol_sets.append(FiniteSet(x))
  
                  start = end
  
              end = domain.sup
              if end in domain and valid(end) and end.is_finite:
                  sol_sets.append(FiniteSet(end))
  
              if valid(_pt(start, end)):
                  sol_sets.append(Interval.open(start, end))
  
              if coeffI != S.Zero and check:
                  rv = (make_real).intersect(_domain)
              else:
                  rv = Intersection(
                      (Union(*sol_sets)), make_real, _domain
                  ).subs(gen, _gen)
  
      return rv if not relational else rv.as_relational(_gen)
  
imports: import itertools
  from sympy.calculus.util import continuous_domain, periodicity, function_range
  from sympy.core import sympify
  from sympy.core.exprtools import factor_terms
  from sympy.core.relational import Relational, Lt, Ge, Eq
  from sympy.core.symbol import Symbol, Dummy
  from sympy.sets.sets import Interval, FiniteSet, Union, Intersection
  from sympy.core.singleton import S
  from sympy.core.function import expand_mul
  from sympy.functions.elementary.complexes import Abs
  from sympy.logic import And
  from sympy.polys import Poly, PolynomialError, parallel_poly_from_expr
  from sympy.polys.polyutils import _nsort
  from sympy.solvers.solveset import solvify, solveset
  from sympy.utilities.iterables import sift, iterable
  from sympy.utilities.misc import filldedent
label_desc: Use image node_id 7 for calling a global function with example usage: solve_univariate_inequality(expr, gen, relational, domain, continuous) and returns: unknown, unknown, rv, r, S, expr