Math, asked by suriyatuition, 9 months ago

Solve for x: |x-1|+|x-2|<3

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Answered by Nivedita4209

Answer:

Think of |a−b||a−b| as the ‘‘‘‘distance”” between the points representing the real numbers aa and bb. So |x−1||x−1| is the distance between xx and 11, and |x−2||x−2| is the distance between xx and 22. Therefore, if xx lies between 11 and 22, |x−1|+|x−2||x−1|+|x−2| is just the distance between 11 and 22. This distance is 11.

If you go either side of these two points 11, 22, by a distance dd, say, the sum of the distances, given by |x−1|+|x−2||x−1|+|x−2|, increases by 2d2d. For xx lying between 11 and 22, the sum of distances equals 11; so we need to consider points that increase this sum by at least 33. For this, we must move at least

Answered by Rohit57RA

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