Question

|a-9|<4

Answer 1

Have you tried separating it into positive case and negative case? :)
(don't forget to reverse the sign in the negative case :D)

Answer 2

|a-9|<4 --> a-9<4 or a-9>-4

Answer 3

no... think of it like this: n whatever is on the left, the number part must be less than 4. forget about sign, just the number part

Answer 4

sorry, not supposed to give it all away.

i think of circle centered at 0 with a radius of 4
now if it's written like this: |a-9|<4 then i think of |a-9| being inside the circle.

and if it's written |a-9|>4 then I think of |a-9| being outside the circle.

Answer 5

the line is just the number line. so all the values inside the circle satisfy the inequality, that is. a - 9 can be any of those numbers.