can anyone tell me how to solve this absolute-value inequality?

State a conjunction or disjunction equivalent to the open sentence.

4 – 2|n + 6| ≥ 2

Please help me through it I don't understand how to do it.

3 Answers

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  • Anonymous
    9 years ago
    Favorite Answer

    1) if n + 6 was positive before absolute-value

    4 - 2(n + 6) ≥2

    4 - 2n - 12 ≥ 2

    4 - 12 - 2 ≥ 2n

    -10 ≥ 2n

    -5 ≥ n

    n ≤ -5

    2) if n + 6 was negative before the absolute-value

    4 - 2(-1)(n + 6) ≥ 2

    4 + 2n + 12 ≥ 2

    2n ≥ 2 - 4 - 12

    2n ≥ -14

    n ≥ -7

    Now we are combining both n ≤ -5 and n ≥ -7

    All values of n are in between -7 and -5, inclusive.

    {all numbers from -7 to -5}

    Source(s): I didn't get the conjuction/disjunction part, have you got the question mixed up?
  • JOS J
    Lv 7
    9 years ago

    -8 <= n <= -4

  • TC
    Lv 7
    9 years ago

    4 - 2In + 6I >= 2

    - 2In + 6I >= - 2

    In+ 6I >= 1

    n + 6 >= 1

    n >= - 5

    - (n + 6) .>= 1

    - n - 6 >= 1

    - n >= 7

    n <= - 7

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