Solve the inequality 1<=abs(2-x)<=5?

1 ≤ |2-x| ≤ 5
1 ≤ |x-2| ≤ 5

|x-2| ≤ 5 AND |x-2| ≥ 1

1)
-5 ≤ x-2 ≤ 5
-3 ≤ x ≤ 7

2)
x-2 ≥ 1 OR x-2 ≤ -1
x ≥ 3 OR x ≤ 1
x ≤ 1 OR 3 ≤ x

1) AND 2)
x ≤ 1 AND -3 ≤ x ≤ 7
OR
3 ≤ x AND -3 ≤ x ≤ 7

-3 ≤ x ≤ 1
OR
3 ≤ x ≤ 7

[-3,1] U [3,7]

|a|=|-a|
|2-x|=|x-2|

{ |x-2|<=5
{ |x-2|>=1

{ -5 <=x-2 <=5
{ x-2 <=-1 V x-2>= 1

S1{ -3 <=x <=7
S2{ x <=1 V x>=3

_______-3____1_______3______7________
S1 ----●___________________●----------
S2___________●-------●_________________

S1intersezione S2
-3 <= x <=1 V 3 <=x <=7.

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