Solve this inequality abs(x-8) > 4?

Question

where abs means absolute value

it also says to express my answer in interval notation...

any thoughts? thanks!!

Answer 1

you just need to solve for x in both directions

because   abs just means distance from zero expressed in positive numbers

viusally it looks like this and doesn't include the number 4, just the point beyond 4 and negative 4

987654...0...456789

now you just have to solve for x

x-8 =-4  and x-8=4

x=4   and x=12

solution set is:

(-I, 4) U (12, I)

I used "I"  because I don't have the code for the infinity symbol

And make sure you use () not [] as 4 and 12 are not included in the solution set.

Answer 2

|x-8| > 4

to solve think that x can either be positive or negative so

solve for -x-8 >4

and for   x-8  >4

the answer is

4>x>12