Answer:
The solution of the given inequality [tex]|x-4|<\:3\:[/tex] is [tex]1<x<7[/tex]
Step-by-step explanation:
Given inequality [tex]|x-4|<\:3\:[/tex]
We have to find the solution of the given inequality [tex]|x-4|<\:3\:[/tex]
Using absolute rule, [tex]\mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a[/tex], we have,
[tex]-3<x-4<3[/tex]
Rewrite as [tex]x-4<-3\quad \mathrm{and}\quad \:x-4<3[/tex]
Consider , [tex]x-4>-3[/tex]
Adding 4 both side, we have,
[tex]x-4+4>-3+4[/tex]
Simplify, we have,
[tex]x>1[/tex]
Consider , [tex]x-4<3[/tex]
Adding 4 both side, we have,
[tex]x-4+4<3+4[/tex]
Simplify, we have,
[tex]x<7[/tex]
Combining, we have,
[tex]1<x<7[/tex]
Thus, The solution of the given inequality [tex]|x-4|<\:3\:[/tex] is [tex]1<x<7[/tex]
