we have
[tex]\left|2x-6\right|<4[/tex]
Solve the inequality
First case
[tex]+(2x-6)<4[/tex]
[tex]2x<4+6[/tex]
[tex]2x<10[/tex]
[tex]x<5[/tex]
The solution of the first case is the interval---------> (-∞,5)
All real numbers less than [tex]5[/tex]
Second case
[tex]-(2x-6)<4[/tex]
[tex]-2x<4-6[/tex]
[tex]-2x<-2[/tex]
[tex]-x<-1[/tex]------->[tex]x>1[/tex]
The solution of the second case is the interval---------> (1,∞)
All real numbers greater than [tex]1[/tex]
The solution of the inequality [tex]\left|2x-6\right|<4[/tex]
(-∞,5) ∩ (1,∞)--------> [tex](1,5)[/tex]
Using a graphing tool
The answer in the attached figure
