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From the bias point, you can have 3V swing up, so you want also 3V swing down (actual collector voltage 3V during negative peak of input signal). So 2V across the emitter is a good starting point.
Neglect Ib, so Re = u/I = 2/0.5m = 4kOhms.
Because of Vbe, Vb will be about 2+0.6 = 2.6V.
Take current through base bias resistors about 10 times Ib (to avoid temperature drift due to temperature dependence of HFE and spread over devices).
Ib = Ic/Hfe = 0.5m/100 = 5uA, so current through bias resistors 50uA.
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