Let k represent some unknown number between -4 and -5. Locate between two consecutive integers the following.?

(A) -k (b) -k +5 (c) k over 2 + 2 (d) k+2 over two

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  • Ron W
    Lv 7
    7 years ago
    Favorite Answer

    -5 < k < -4

    (a)

    Multiply all three parts by -1. Since -1 is negative, this will reverse the sense of the inequalities:

    5 > -k > 4

    or equivalently

    4 < -k < 5

    -k is between 4 and 5.

    (b)

    Add 5 to all three parts of my answer to (A):

    4 < -k < 5

    9 < -k + 5 < 10

    -k + 5 is between 9 and 10

    (c)

    I assume this means (k/2) + 2, not k(2+2)

    -5 < k < -4

    Divide all 3 parts by 2. Since 2 is positive, the sense of the inequalities is preserved:

    -5/2 < k/2 < -2

    -1/2 < (k/2) + 2 < 0

    Therefore, k is between -1 and 0.

    (d)

    -5 < k < -4

    Add 2 to all three parts:

    -3 < k + 2 < -2

    Divide all three parts by 2. Since 2 is positive, the sense of the inequalities is preserved:

    -3/2 < (k + 2)/2 < -1

    so (k + 2)/2 is between -2 and -1.

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