# During an illness, a patient's body tempT satisfied the inequality |T - 98.6| £ 2. Find lowest temp patient could have had during llness.

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l T - 98.6 l =< 2

That means the absolute difference between the patient tempreture and the ideal temp. should not exceed 2 degrees difference:

Let us solve the inequality:

l T - 98.6 l =< 2

==> (T - 98.6) =< 2 OR - (T-98.6) =< 2

==> T =< 100. 6 OR -T + 98.6 =< 2

==> T =< 100.6 OR T >= 96.6

==> 96.6 =< T =< 100.6

**Then the lowest temp for the patient should be 96.6, and the hieghst is 100.6**

The temperature of the patient is given by the relation, |T-98.6| < = 2.

To find the lowest temperature the patient had during the illness.

|T-98.6| < = 2

Therefore for T > 98.6 , the relation is T -98.6 < = 2. Or

T < = 96.6+2 = 98.6 . But this solution of T is not giving us the required information , as it gives the information of maximum temperature.

So we gor for T < = 98.6.

When T< =98.6 , the relation |T-98.6| < 2 implies 98.6 -T < 2. Or

98.6 - T+T < = 2+T.

98.6 < =2+T

98.6 -2 < = 2-2 +T

96.6 < = T.

Therefore this gives the information that lowest temperature the patient had was 96.6 during his illness.