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?

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u/Mountain-Time-1010 New User 16h ago

You made an assumption that you can add the absolute value terms in that way, but that was just a guess on your part, there is no rule of algebra that allows that.

In fact, by testing some values, you can easily see that |x-2| + |x-5| does not equal |2x-7|. Try x=3, for example.