Solution for 1:
2x > -6 and x - 4 < 3
Simplifying gives x > -3 and x < 7
Combining the two equations gives;
-3 < x < 7
Solution for 2:
x + 5 > 2x + 1 and -4x < -8
Simplifying the two equations gives;
5 > x and x < 2
Combining them together gives;
x < 2 and 5
Solution for 3:
-3x < -6 or x + 5 < -2
Simplifying the two equations gives;
x < 2 or x < 7
Combining the two equations gives;
x < 2 or 7
Solution for 4:
x - 2 > 2x + 1
or
-2x - 2 < 10
Simplifying the two equations gives;
-3 > x or x < -6
Combining the equations gives;
x < -3 or -6
Solution for 5:
-4 < 2x - 8 < 6
Simplifying gives;
-4 < 2x < 14
Dividing by 2 throughout gives;
-2 < x < 7