Subject

    গাণিতিক যুক্তি

    Topic

    অসমতা

    |x| > 3

    ক)
    -3 > x > 3
    খ)
    2 > x > 3
    গ)
    3 > x > 3
    ঘ)
    4 > - x > 3

    Explanation

    The absolute value inequality ∣x∣>3|x| > 3 means the distance of xx from zero on the number line must be greater than 3. This translates to xx being either less than −3-3 or greater than 33. The correct option, −3>x>3-3 > x > 3, is actually a typo in the input provided, as the standard representation for this solution set is x<−3x < -3 or x>3x > 3, which is sometimes written incorrectly as −3>x>3-3 > x > 3 in some contexts when the intent is to describe the two separate regions. However, based on the provided correct answer format, we must assume it represents the solution set where xx is outside the range [−3,3][-3, 3]. Options B, C, and D clearly mismatch: Option B (2>x>32 > x > 3) describes a range between 2 and 3, Option C (3>x>33 > x > 3) is impossible as xx cannot be strictly less than 3 and strictly greater than 3 simultaneously, and Option D (4>−x>34 > -x > 3) is equivalent to −4<x<−3-4 < x < -3.

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