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4 November, 21:43

What's the inequality for |u|-2<5

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  1. 4 November, 22:00
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    0 ≤ u u > - 7 and combining those two we get - 7 < u < 7.

    Step-by-step explanation:

    The given inequality is |u| - 2 < 5 ... (1)

    We have to solve this inequality.

    Now, from the definition of f (x) = |x| we get, f (x) = x, when x ≥ 0 and

    f (x) = - x when x < 0.

    Hence, for u ≥ 0, the equation of inequality (1) becomes

    u - 2 < 5

    ⇒ u < 7

    Therefore, the solution is 0 ≤ u < 7 (Answer)

    Again, for u < 0, the equation of inequality (1) becomes

    - u - 2 < 5

    ⇒ u + 2 > - 5

    ⇒ u > - 7

    Therefore, the solution becomes 0 > u > - 7 (Answer)
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