The sum of four consecutive odd integers is –72. Write an equation to model this situation, and find the values of the four integers. A. n – (n + 2) – (n + 4) – (n + 6) = –72; n = –20; n + 2 = –18; n + 4 = –16; n + 6 = –14 B. n + (n – 2) + (n – 4) + (n – 6) = –72; n = – 21; n – 2 = –23; n – 4 = –25; n – 6 = – 27 C. n + n + 2 + n + 4 + n + 6 = –72; n = –21; n + 2 = –23; n + 4 = –25; n + 6 = –27 D. n + n + 2 + n + 4 + n + 6 = –72; n = –21; n + 2 = –19; n + 4 = –17; n + 6 = –15

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DarcySea DarcySea · Answer 1 · 2019-11-13T03:15:02+01:00

Answer:

D. [tex]n + n + 2 + n + 4 + n + 6 = -72; n = -21; n + 2 = -19; n + 4 = -17;n + 6=-15[/tex]

Step-by-step explanation:

Given:

The sum of four consecutive odd integers is -72.

Let the 4 consecutive odd integers be [tex]n,n+2,n+4,\textrm{ and }n+6[/tex]

Now, as per question,

[tex]n + (n + 2) + (n + 4) + (n + 6) = -72\\n+n+n+n+2+4+6=-72\\4n+12=-72\\4n=-72-12\\4n=-84\\n=-\frac{84}{4}=-21[/tex]

Therefore, the consecutive integers are:

[tex]n=-21\\n+2=-21+2=-19\\n+4=-21+4=-17\\n+6=-21+6=-15[/tex]

Hence, the correct option is option D.