Question 919339

Consecutive integers are only {{{1}}} away from each other. So, if you let the first integer be {{{x}}}, the second is {{{x+1}}} and the third is {{{x+2}}}. 

if their sum is {{{-75}}}, then we have:

{{{x+(x+1)+(x+2)=-75}}}

{{{x+x+1+x+2=-75}}}

{{{3x+3=-75}}}

{{{3(x+1)=-75}}}

{{{x+1=-75/3}}}

{{{x+1=-25}}}

{{{x=-25-1}}}

{{{highlight(x=-26)}}}

so, 

first integer is {{{highlight(x=-26)}}}, 

second integer is {{{x+1=-26+1}}}=>{{{highlight(x+1=-25)}}} and

third integer is {{{x+2=-26+2}}}=>{{{highlight(x+2=-24)}}}

check their sum:

{{{(-26)+(-25)+(-24)=-75}}}

{{{(-51)+(-24)=-75}}}

{{{-75=-75}}}