write 5<x<11 in form /x-a/<b, use A.=11+5/2 and B.=11-5/2

Question

exercise 1 of our collage algebra

Answer 1

|x-a|<b means x-a<b or a-x<b; so x<a+b or x>a-b. 5<x<11 means x>5 and x<11.

So, a-b=5 and a+b=11; add these equations together: 2a=16, so a=8 and b=3 and |x-8|<3.

A. x=(11+5)/2=8. Plug this in: |x-8|=0 which is less than 3 and B. x=(11-5)/2=3. Plug this in: |x-8|=|-5|=5 which is not less than 3. So A satisfies the inequalities but B doesn't.