Answer:
The numbers are -14,-13 and -12
Step-by-step explanation:
The correct question is
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
[tex]x+2(x+1)+3(x+2)=-76[/tex]
solve for x
apply distributive property
[tex]x+2x+2+3x+6=-76[/tex]
Combine like terms
[tex]6x+8=-76[/tex]
subtract 8 both sides
[tex]6x=-76-8[/tex]
[tex]6x=-84[/tex]
Divide by 6 both sides
[tex]x=-14[/tex]
so
[tex]x+1=-14+1=-13[/tex]
[tex]x+2=-14+2=-12[/tex]
therefore
The numbers are -14,-13 and -12
