Treatment of Ineqality Vs Equation

[KK]

I had been treating eqality sign like an equation.

such as:

X(X+1) > 0, i was treating this as a way we deal with equation such as x> 0 and x+1 > 0 , however came to know its not true.

3^x < 3^2x and finally saying x< 2x ( dont know if its wrong)

Please tell me if there are some rules to avoid such confusion.

Please help else i am getting all questions wrong.

[RonPurewal]

I had been treating eqality sign like an equation.

such as:

X(X+1) > 0, i was treating this as a way we deal with equation such as x> 0 and x+1 > 0 , however came to know its not true.

3^x < 3^2x and finally saying x< 2x ( dont know if its wrong)

Please tell me if there are some rules to avoid such confusion.

Please help else i am getting all questions wrong.

read this answer to your other post.
if you have a function that always increases with increasing x, such as exponential functions, then you can do this. so yes, if 3^(2x) is greater than 3^x, then 2x must be greater than x.
for the inequality you've provided, x(x + 1) > 0, the left-hand (left of -1) and right-hand (right of 0) regions work, so the solution would be x < -1 or x > 0.

by contrast, x(x + 1) is a quadratic function, which decreases and then increases, so the inequality isn't that simple. instead, you would solve the associated equation, x(x + 1) = 0, then put the solutions (-1 and 0) on a number line. those solutions divide the number line up into three regions (left of -1, between -1 and 0, right of 0); you'd test each of the three regions individually, see whether it works, and then put the solution set together from the ones that do work.