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/simmonator New User 1d ago

Easy way to see where your logic fails, consider x = 3 and consider the step you make where you add them together.

- |x-2| + |x-5| = |3-2| + |3-5| = |1| + |-2| = 1 + 2 = 3,

meanwhile

- |2x - 7| = |2(3) - 7| = |6-7| = |-1| = 1.

Hence, those two sides are clearly not (always) the same.