What’s the inequality for this problem?

The answers for the exercise shown in the figure attached above, are shown 

 -The Compound inequality for the solution 1 is:
 -2(x+1)≥-4 or 4x-7≥5
 x≥1
 x≥3
 -The Compound inequality for the solution 2 is:
 -6≤2x-8≤-2
 1≤x≤3
 -The Compound inequality for the solution 3 is:
 3x-4≥5 or -5x+17≤12
 x≥3
 x<1