solving equation involving absolute values

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Sage uses other programs for many of its functionality. In symbolic calculus Sage relies on Maxima for doing integrals, ODEs, limits, equations, simplifications and other things. Equation solving uses Maxima's core but this has limited functionality. Maxima itself in turn makes use of additional packages to augment its abilities.

If you type:

sage: solve??

you see among other things:

-  ``to_poly_solve`` - bool (default: False) or string; use
   Maxima's ``to_poly_solver`` package to search for more possible
   solutions, but possibly encounter approximate solutions.
   This keyword is incompatible with ``multiplicities=True``
   and is not used when solving inequalities. Setting ``to_poly_solve``
   to 'force' (string) omits Maxima's solve command (useful when
   some solutions of trigonometric equations are lost).