Answer:
The integers are -5, -3 and -1.
Explanation:
Let the first consecutive odd integer = x
• Then the next two consecutive odd integers = x+2 and x+4
The sum of the three integers is:
[tex]x+(x+2)+(x+4)=3x+6[/tex]
4 times the sum of three consecutive odd integers:
[tex]\implies4(3x+6)[/tex]
The result is -36. Thus, we have the equation:
[tex]4(3x+6)=-36[/tex]
Solve for x:
[tex]\begin{gathered} 3x+6=\frac{-36}{4} \\ 3x+6=-9 \\ 3x=-9-6 \\ 3x=-15 \\ x=-\frac{15}{3} \\ x=-5 \end{gathered}[/tex]
Thus, the integers are:
[tex]\begin{gathered} x=-5 \\ x+2=-5+2=-3 \\ x+4=-5+4=-1 \end{gathered}[/tex]
The integers are -5, -3 and -1.
