Lisa spends a total of 4 * 2 = <<4*2=8>>8 hours on her two classes.
She has a total of 168 - 8 - 21 = <<168-8-21=139>>139 hours left for sleep and work.
To get her sleep, she can sleep a maximum of 8 * 7 = <<8*7=56>>56 hours in a week.
So, she has 139 - 56 = <<139-56=83>>83 hours left for work.
Therefore Lisa can work a maximum of 83 hours each week. Answer: \boxed{83}.
Lisa is taking two classes at a local community college. She sets aside 21 hours for homework a week with these two classes. The two classes are 4 hours each once a week on Tuesday and Thursday. She wants to get a part time job and ensure 8 hours of sleep each night. There are 168 hours in one week. How many hours can she work at most each week? Write and solve an inequality to determine the maximum amount of time she can work each week.
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