Generally speaking, they are all constructed by monotonicity of functions, because monotone functions can compare the values of one or two functions, and solving inequalities is to solve them through known inequalities, so they are very compatible. It should be to construct a simple or characteristic function so that its function value at a special point is equal to the value of one side of the inequality with a simple form, and the other side is basically what the function needs to construct (because the situation is complicated, it is basically the shape of the function to be constructed), or the two sides of the inequality are similar in form, in which case the function must be in this form.

The above is just a simple statement. If you have specific questions, you can ask them above ~

When you first start learning, you will naturally find it a bit difficult. You will get better gradually, don't worry ~