Answer:
The numbers are -14,-13 and -12
Step-by-step explanation:
<u><em>The correct question is </em></u>
Find three consecutive integers such that the sum of the first, twice the second and three times the third is -76. What is the number?
Let
x ----> the first consecutive integer
x+1 ---> the second consecutive integer
x+2 ---> the third consecutive integer
we have that
![x+2(x+1)+3(x+2)=-76](https://tex.z-dn.net/?f=x%2B2%28x%2B1%29%2B3%28x%2B2%29%3D-76)
solve for x
apply distributive property
![x+2x+2+3x+6=-76](https://tex.z-dn.net/?f=x%2B2x%2B2%2B3x%2B6%3D-76)
Combine like terms
![6x+8=-76](https://tex.z-dn.net/?f=6x%2B8%3D-76)
subtract 8 both sides
![6x=-76-8](https://tex.z-dn.net/?f=6x%3D-76-8)
![6x=-84](https://tex.z-dn.net/?f=6x%3D-84)
Divide by 6 both sides
![x=-14](https://tex.z-dn.net/?f=x%3D-14)
so
![x+1=-14+1=-13](https://tex.z-dn.net/?f=x%2B1%3D-14%2B1%3D-13)
![x+2=-14+2=-12](https://tex.z-dn.net/?f=x%2B2%3D-14%2B2%3D-12)
therefore
The numbers are -14,-13 and -12