|f(x)| is equivalent to 2 equations
f(x) when f(x) >= 0 OR -f(x) when f(x)< 0
so |x-11| > 4 is equivalent to
x-11 > 4 when x-11 >= 0 OR
-(x-11) > 4 when x-11 < 0
rearrange
x-11 > 4 when x-11 >= 0 we get
x > 15 when x >= 11 ... means x > 11
-(x-11) > 4 when x-11 < 0 we get
x < 7 when x < 11 ...means x < 7
so we have. x < 7 OR x > 11 for this inequality which is not the correct answer
... now... what is solution for |x-11| < 4
you can try to work as above and should come up with the solution just 'the opposite' which is x > 7 OR x < 11 [ 7 < x < 11 ]
then you work for c) and could work or guess for d)
