We have 2 + x < 6
⇒2 + x −2< 6−2
⇒x<4
Now 2−3x<−1⇒2−3x−2<−1−2⇒−3x<−3⇒−3x−3>−3−3⇒x>1
Hence the solution of the given system of equations is given by 1<x<4,xϵZ⇒x=2,3
Hence solution set is [7,∞)⋂(−∞,1)=ϕ
which implies no solution exists.
Hence the solution set is [−4,∞)⋂(−∞,1]=[−4,1]
Which means − 4 ≤ x ≤ 1