To determine the smallest of the three consecutive integers whose sum is -75, let's denote the integers as [tex]\( x \)[/tex], [tex]\( x+1 \)[/tex], and [tex]\( x+2 \)[/tex].
1. The sum of these three consecutive integers can be written in equation form:
[tex]\[ x + (x+1) + (x+2) = -75 \][/tex]
2. Simplify the left-hand side:
[tex]\[ x + x + 1 + x + 2 = -75 \][/tex]
[tex]\[ 3x + 3 = -75 \][/tex]
3. Subtract 3 from both sides of the equation to isolate terms involving [tex]\( x \)[/tex]:
[tex]\[ 3x = -75 - 3 \][/tex]
[tex]\[ 3x = -78 \][/tex]
4. Divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-78}{3} \][/tex]
[tex]\[ x = -26 \][/tex]
Hence, the smallest of the three consecutive integers is:
\[ \boxed{-26}
