Explain Inequalities

1)
2x > -6 and x - 4 ≤ 3
x > -6/2 and x ≤ 3 + 4
x > -3 and x ≤ 7

2)
-6 < x + 3 < 6
-6 - 3 < x < 6 - 3
-9 < x < 3

3)
x - 2 ≥ 2x + 1 or 10 > -2x + 2
x - 2x ≥ 2 + 1 or -2x < 10 - 2
-x ≥ 2 or -2x < 8
x ≤ 2/-1 or x > 8/-2
x ≤ -2 or x > -4

Explaining a problem? News to me! Do you mean you want to know how to solve it or what kind of explanation you need on the problem itself. Please be more specific. 2x > - 6 is same as x> - 3 or - 3<x
x - 4 <_3 is same as x <_7 so both put together means - 3<x<_7.
Rest are in a similar manner.
You have only to remember that an inequality should not be devided or multiplied by a - ve number.

I'm not exactly sure what you mean by "explain", but bskelkar is wrong about one thing, you CAN "divide" and multiply inequalities by negative numbers, it's just that when you do, you flip the sign.