Answer:
[tex]|x - 98.6| > 1.5[/tex]
Step-by-step explanation:
Given
Temperature = 98.6F
Range = 1.5F
Required
Write the absolute value inequality
Let the temperature be represented by x
We start by writing an expression for the difference between x and 98.6.
This can be written as x - 98.6
From the question, we understand that this difference is more than 1.5F
Representing this using absolute value inequality; we have
[tex]|x - 98.6| > 1.5[/tex]
Solving further; this gives
[tex]x - 98.6 > 1.5[/tex] or [tex]x - 98.6 < -1.5[/tex]
Make x the subject of formula in both cases
[tex]x >98.6 +1.5[/tex] or [tex]x < 98.6-1.5[/tex]
[tex]x >100.1[/tex] or [tex]x < 97.1[/tex]
This can be rewritten as
[tex]x >100.1[/tex] or [tex]97.1>x[/tex]
Combining these two inequalities;
[tex]97.1 > x > 100.1[/tex]
Hence;
The absolute inequality is [tex]|x - 98.6| > 1.5[/tex]
And the range of value is [tex]97.1 > x > 100.1[/tex]
