As above acetone is not in any sense a "glue" what it will do is melt the plastic edge you apply it to, then when you press the two edges together they will "flow" together. A bit like what occurs in welding. Just be careful as too much will soften the plastic to a point that it will not harden again. So small amounts, apply with a paint brush of something similiar, and 24hrs to reharden the melted-together edges. Soft heat and air flow will aid the process.
Again caution with the acetone. Vapors will ignite so don't work near sparks or flame (like a basement water heater)