For this case we have to:
Integer 1: Represented with the variable[tex]x[/tex]
Integer 2: It is consecutive, then it is represented with [tex]x + 1[/tex]
We propose the equation:
[tex]3x + 2 (x + 1) = 27[/tex]
We apply distributive property to the terms within parentheses:
[tex]3x + 2x + 2 = 27[/tex]
We add similar terms:
[tex]5x + 2 = 27[/tex]
We subtract 2 from both sides:
[tex]5x = 27-2\\5x = 25[/tex]
We divide between 5 on both sides:
[tex]x = \frac {25} {5}\\x = 5[/tex]
Finally we have to:
[tex]x = 5\\x + 1 = 5 + 1 = 6[/tex]
ANswer:
Consecutive integers are 5 and 6
