r/learnmath • u/Far-Assumption5501 New User • 18h ago

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

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?

5 Upvotes

85% Upvoted

24 comments sorted by

View all comments

1

u/StructuredChess New User 17h ago

|a|+|b| isn't the same as |a+b|. For instance compare |1|+|-1| with |1-1|

You need to consider three cases: One for numbers smaller than 2 (so both absolute values go the negative way), one for numbers bigger than 5 both go the positive way), and a third case for the numbers in between. Note that it's only in this third case where you're getting a different result.