Verified answer

|x^2 - 10| ≤ 6

=> - 6 ≤ x^2 - 10 ≤ 6

=> 4 ≤ x^2 ≤ 16

=> 2 ≤ l x l ≤ 4

2 ≤ l x l

=> l x l ≥ 2

=> x ≥ 2 or ≤ - 2 ... ( 1 )

l x l ≤ 4

=> - 4 ≤ x ≤ 4 ... ( 2 )

Intersection of ( 1 ) and ( 2 )

=> x ∈ [- 4, - 2] U [ 2, 4 ].

The inequality is equivalent to

x^2-10 ≤ 6 => -4 ≤ x ≤ 4

and

-x^2+10 ≤ 6 => 4 ≤ x^2 => x ≤ -2 or 2 ≤ x

Conjunction: (-4 ≤ x ≤ 4) and (x ≤ -2 or 2 ≤ x)

Answer: -4 ≤ x ≤ -2 or 2 ≤ x ≤ 4

x ≤ 4,-4