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infact .. when u see x is < or> than the negetive number the sign get changed .. imean in this case.. if x >-2 then it gets -2<x<7....then its not true to say x>2 st choice is wrong.. _________________

I think there is an error in the original problem. I've seen a few problems like this one and the problem you posted doesn't make sense. Could you verify it?

if it is true that x> -2 and x>7 ,which of the following must be ture?
Now the values of x that will always satisfy above 2 inequalities will be:
x > 7.
Seems like choices are messed up.

Tips on inequalities (basics):
1) Multiply an inequality by a negative number and sign of inequality changes, for eg:
x < -2
or -x > 2 (multiply both sides by -1)

2) If two set of numbers a,b & x,y are positive
and x*a > y*b such that x < y
then a > b ( i remember seeing one question that tested this)
for example:
3*x^2 > 4*y^2 (here x^2, y^2 are positive numbers -squares)
Then, X^2 > Y^2

whereas, if 4*x^2 > 3*y^2
Then, i cannot conclude anything..!!

If X, Y are average of two sets of data then X, Y are always positive.

3) Mutiplying by a positive number, adding or subtracting any number (positive or negative) [u]does't change the sign of inequality.[/u]For example:
3 > -5 -----------a
then 9 > -15 (3 mutiplied on both sides of eq a)
Also, 0 > -8 (3 subtracted from both sides of eq a)
Also, 6>-2 (3 added on both sides of eq a)