Answer & Step-by-step explanation:
Okay, so to find all the values for x, solve the equation for x first (it's kind of long and didn't fit, sorry)
[tex]y=|x-1|-2\\\\x=-y-1,y+3[/tex]
Then find the range for x based on the two equations of -y-1 and y+3. Since this is an odd-degree polynomial, the range is all real numbers:
[tex]x[/tex] ∈ [tex]R[/tex]
(x is all real numbers)
Unless....
Take the given inequality [tex]|x-1|-2<0[/tex] and find the range:
Add two to both sides:
[tex]|x-1|-2+2<0+2\\|x-1|<2[/tex]
Rewrite without the absolute value:
[tex]-2<x-1<2[/tex]
Add 1 to the whole equation:
[tex]-2+1<x-1+1<2+1\\\\-1<x<3[/tex]
Maybe don't trust me..
