|
Question 1168629: solve |x+2|<|x-5|
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
This problem is for advanced Math students.
I will give you an idea only, leaving its implementation on you.
You should consider 3 intervals on the number line, created by 2 (two) critical points.
The points are -2 and 5; they are vertices of the functions.
The intervals are (-oo,-2), (-2,5) and (5,oo).
In each of these intervals the given functions are linear - - - you should represent these LINEAR functions
in each of the intervals SEPARATELY.
You will get 3 inequalities: one for each interval.
You should solve these three separate inequalities SEPARATELY.
For each of these inequalities, you should check if the solution BELONGS to the relevant interval.
This work includes many details to analyze on the way, but having these global instructions,
an advanced student should be able to proceed to the end.
To avoid mistakes, it is be VERY HELPFUL to have the plot of the left and the right side in one plot in front of you.
--------------
As always in difficult cases, I have good references for you.
See the lessons
- Absolute Value equations
- HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 1
- HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 2
- HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 3 (*)
- HOW TO solve equations containing Quadratic Terms under the Absolute Value sign. Lesson 1
- HOW TO solve equations containing Quadratic Terms under the Absolute Value sign. Lesson 2
- OVERVIEW of lessons on Absolute Value equations
in this site.
Read them attentively and become an expert in this area.
Play special attention to the lesson marked (*) in the list: it is most relevant to your problem.
But to understand the subject in whole, you better look into ALL these lessons.
You NOWHERE in accessible literature in English will find this material taught in so compact and clear form.
|
|
|
| |
