Assuming that 99.1℉ is a temperature rounded to 1 decimal place then the true temperature T must satisfy T<99.15 and T>99.05, that is, 99.05<T<99.15 (ignoring the traditionally accepted rule for rounding T≥99.05).
To express this as an absolute value inequality we subtract 99.1 from each term in the multiple inequality:
-0.05<T-99.1<0.05. This is now in the form ready to be converted to an absolute value inequality:
|T-99.1|<0.05. The range of values of T making this true is shown graphically below.
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