(2) inequality | ax+b | ≥ c (c >; 0): Firstly, it is transformed into a set of inequalities ax+b≤-c and ax+b≥c, and then the solution set of the original inequality is obtained by using the properties of the inequality.
The core task of a famous teacher to solve an inequality with absolute value is to remove the absolute value, transform the inequality into a conventional inequality without absolute value, and then solve it by using the mastered problem-solving methods; Be careful not to square the absolute value sign blindly.
4. Solutions of inequalities of type | x-a | +| x-b |≥ c and | x-a |+| x-b |≤ c.
Option 1: You can use the geometric meaning of absolute value.
Scheme 2: Using the idea of classified discussion, the number axis is divided into several intervals with the "zero" of absolute value as the dividing point, and then the symbol of polynomial in each absolute value is determined, and then the absolute value symbol is removed (referred to as subsection discussion method)
Solution 3: By constructing the function and using the function image (image method for short), the solution set of inequality can be obtained.
As can be seen from the above, the key to solving the inequality with absolute value lies in using the meaning of absolute value, trying to remove the absolute value sign and transform it into one or several ordinary inequalities or a group of inequalities (that is, inequalities without absolute value sign).
In particular, the absolute value inequalities | x-a |-x-b |≤ c and | x-a |-x-b |≥ c can also be solved by the above three methods.