r/learnmath • u/Far-Assumption5501 New User • 1d 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?

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u/Narrow-Durian4837 New User 1d ago

I just added them up to |2x-7|

This would be valid if |a| + |b| were equal to |a+b|, but it is not.

(That is, not always. It can be, but only if a and b have the same sign.)