we call the first number: x
The next even integer will be: x+2
And the third even integer: x+4
Note: from the first number 2 the second number we add two, because even numbers are 2 numbers apart, for example 2 and 4, 4 and 6, etc.
We are told that the sum of the three numbers is -102, thus, we add the numbers and equal them to -102:
[tex]x+x+2+x+4=-102[/tex]On the left side, we combine like terms:
[tex]3x+6=-102[/tex]Next, we substract 6 from both sides:
[tex]\begin{gathered} 3x+6-6=-102-6 \\ 3x=-108 \end{gathered}[/tex]And now we divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{-108}{3} \\ x=-36 \end{gathered}[/tex]Since we knoe x, we can find the numbers:
First number: x ----> -36
Second number: x+2 ---> -36+2=-34
Third number: x+4 ---> -36+4=-32
Smallest number: -36
Middle number: -34
Largest number: -32
