1.) 2x > - 6 and x - 4 < 3

2.) x + 5 > 2x + 1 and - 4x < - 8

3.) - 3x < - 6 or x + 5 < - 2

4.) x - 2 > 2x + 1 or - 2x - 2 < - 10

5.) - 4 < 2x - 8 < 6

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