Using sympy to solve a two-sided inequality with absolute value

Question

Relatively simple math problem, find the range over which 3 <= Abs[6 - x] <= 5. Not hard to solve by hand, and Mathematica nails it, with the answer 1 <= x <= 3 || 9 <= x <= 11.

The closest I can get with sympy is

from sympy import *
x = symbols('x', real=True)
reduce_inequalities([3 <= abs(6 - x), abs(6 - x) <= 5], x)

This results in

1≤∧≤11∧(9≤∨≤3)

which, if I read it correctly, is sympy's way of saying

1 <= x || x< 11 || (9 <= x || x <= 3)

which is both odd and wrong. What am I missing here?

Answer 1

This is the output from SymPy:

In [1]: from sympy import *
   ...: x = symbols('x', real=True)
   ...: reduce_inequalities([3 <= abs(6 - x), abs(6 - x) <= 5], x)
Out[1]: 1 ≤ x ∧ x ≤ 11 ∧ (9 ≤ x ∨ x ≤ 3)

What this means is that 1 <= x <= 11 AND (x >= 9 OR x <= 3).

This is logically equivalent to the Mathematica output that you refer to although perhaps not expressed as clearly. You can manipulate the output to the same form with:

In [2]: r = reduce_inequalities([3 <= abs(6 - x), abs(6 - x) <= 5], x)

In [3]: r.as_set()
Out[3]: [1, 3] ∪ [9, 11]

In [4]: r.as_set().as_relational(x)
Out[4]: (1 ≤ x ∧ x ≤ 3) ∨ (9 ≤ x ∧ x ≤ 11)