# "Let the smallest of these odd integers be:" \qquad \qquad 2 n - 1. #

# "The remaining 4 odd integers are:" #

# \qquad \qquad \qquad \qquad \qquad \quad \ 2 n + 1, \quad 2 n + 3, \quad 2 n + 5, \quad 2 n + 7. \quad #

# "The average of all 5 odd integers is:" #

# { ( 2 n - 1 ) + ( 2 n + 1 ) + ( 2 n + 3 ) + ( 2 n + 5 ) + ( 2 n + 7 ) } / 5. #

# "The average of all 5 odd integers is given to be -21. Thus:" #

# { ( 2 n - 1 ) + ( 2 n + 1 ) + ( 2 n + 3 ) + ( 2 n + 5 ) + ( 2 n + 7 ) } / 5 #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad \quad = -21. #

# \qquad \qquad \qquad \qquad \qquad { 5 ( 2 n ) - 1 + 1 + 3 + 5 + 7 } / 5 \ = \ -21 #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad { 10 n + 15 } / 5 \ = \ -21 #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ { color{red}cancel{ 5 } ( 2 n + 3 ) } / color{red}cancel{ 5 } \ = \ -21 #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ 2 n + 3 \ = \ -21 #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad \ \ 2 n \ = \ -21 - 3 #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad \ \ 2 n \ = \ -24 #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad \ \ \ \ n \ = \ -12. #

# "At the start here, we had:" #

# \qquad \qquad \quad \ "the smallest of these odd integers is:" \qquad \quad 2 n - 1. #

# "As we found" \quad n \ = -12, \ "we have:" #

# \qquad \qquad \quad \ "the smallest of these odd integers is:" #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad = \ 2 ( -12 ) - 1 #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad = \ -24 - 1 #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad = \ -25. #

# "This is our answer:" \qquad \qquad \qquad -25. \qquad \qquad \qquad \qquad \qquad \qquad !! #