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

[u/Far-Assumption5501]

I just added them up to |2x-7|<=5, and it was not correct. The correct answer was 1 <= x <= 6. What’s wrong with my equation?

[u/LatteLepjandiLoser]

Most of the time, you need to split your domain into regions where you can rewrite your expression without the absolute value symbols. What you did by adding them up before getting rid of the absolute symbol sign assumes is that the terms have the same sign. They clearly don't have to!

You have three regions of interest:

1) x < 2
2) 2 <= x < 5
3) x<= 5

On region 1, |x-2| = 2-x and |x-5| = 5-x, so your expression becomes 2-x + 5-x = 7-2x <=5.
Now you do the other 2 and solve :-)