The expression 9n + 1 represents the perimeter (in meters) of
the triangle. write an expression in simplest form that represents the measure of the third side.

The expression 9n + 1 represents the perimeter

sum of the sides of the triangle, equal to the perimeter:    

                                                                          x +  3n+2 + 2n-1 = 9n + 1

                                                                                    x +  5n + 1 = 9n + 1

                                                                                                   x = 9n +1 - 5n -1

                                                                                     x= 4n

Remove the parentheses from the equation:

Combine like terms:

The greatest common factor (GCF) of both terms is 8, so we can divide the entire expression by 8 and move it outside parentheses:

The simplified form of this expression is 8(r - 1).