Peter asked in Science & MathematicsMathematics · 7 years ago

# 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

-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.