Answer: The total distance for which the bike was tested is [tex](x^2+5x)~\textup{miles}.[/tex]
Step-by-step explanation: Given that a sports company conducted a road test of a new model of a geared bike.
The test rider cycled [tex](3x-2)[/tex] miles on a flat road, [tex](x^2-5)[/tex] miles uphill and [tex](2x+7)[/tex] miles downhill.
We are to find the simplified expression that is equivalent to the total distance, in miles, for which the bike was tested.
The total distance for which the bike was tested is given by
[tex]D\\\\=(3x-2)+(x^2-5)+(2x+7)\\\\=3x-2+x^2-5+2x+7\\\\=x^2+5x.[/tex]
Thus, the total distance for which the bike was tested is [tex](x^2+5x)~\textup{miles}.[/tex]
