Answer:
[tex]6.7<x<9.7[/tex].
Step-by-step explanation:
We have been given an inequality [tex]|x-8.2|-1.5<0[/tex] and we are asked to solve our given inequality.
Let us add 1.5 to both sides of our inequality.
[tex]|x-8.2|-1.5+1.5<0+1.5[/tex]
[tex]|x-8.2|<0+1.5[/tex]
Upon using definition of absolute value function [tex]|f(x)|<a\Rightarrow f(x)<a \text{ and } f(x)>-a[/tex] we can write our absolute function as:
[tex]x-8.2<1.5\text{ and } x-8.2>-1.5[/tex]
[tex]x<1.5+8.2\text{ and } x>-1.5+8.2[/tex]
[tex]x<9.7\text{ and } x>6.7[/tex]
Upon combining our ranges we will get,
[tex]6.7<x<9.7[/tex]
Therefore, our inequality solves to [tex]6.7<x<9.7[/tex].
