Thread: When? does the inequality solve

In what cases would you have to change the inequality sign?

I mean, if you have an equation like,

|x| + |2x-5| < 5

You would have 3 cases right?

So what would the sign (< and >) look like for those 3 and why does it change some times?

Originally Posted by Freaky-Person

In what cases would you have to change the inequality sign?

I mean, if you have an equation like,

|x| + |2x-5| < 5

You would have 3 cases right?

So what would the sign (< and >) look like for those 3 and why does it change some times?

The traditional way you are taught in high-schools, that means look at the plus minus signs DOES NOT WORK in general. It only works in the problems they give you.
This happens to be a more advanced problem.
We need to use the following definition,

Thus, we the the following cases,

And it depends on,
Also we have,

And it depends on,
Solve the inequality,
and .
In combination with,
and .
We have the following cases,

1)
and

2)
and

3)
and .

Thus, consider the inequality

If, the first case,




But that is a contradiction because .
If, the second case,




This will be a contradiction unless
If, the third case,




This will be a contradiction unless
Thus,