Parse the date:
Date myDate = dateFormat.parse(dateString);
And then either figure out how many milliseconds you need to subtract:
Date newDate = new Date(myDate.getTime() - 604800000L); // 7 * 24 * 60 * 60 * 1000
Or use the API provided by the java.util.Calendar
class:
Calendar calendar = Calendar.getInstance();
calendar.setTime(myDate);
calendar.add(Calendar.DAY_OF_YEAR, -7);
Date newDate = calendar.getTime();
Then, if you need to, convert it back to a String:
String date = dateFormat.format(newDate);
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