Question

A sports company conducted a road test of a new model of a geared bike. The test rider cycled (3x - 2) miles on a flat road, (x2 - 5) miles uphill, and (2x + 7) miles downhill. Which simplified expression is equivalent to the total distance, in miles, for which the bike was tested?

x2 - x

x2 + 5x

x2 − x + 14

x2 + 5x + 14

Answer 1

(5x2 + 3x + 4) − (2x2 + 5x − 1) =
5x2 + 3x + 4 − 2x2 - 5x + 1 =
5x2 - 2x2 + 3x - 5x + 4 + 1 =
3x2 - 2x + 5.

A = 3, B = -2, C = 5

2)
Total Distance = Flat Road Distance + Uphill Distance + Downhill Distance
= (3x - 2) + (x2 - 5) + (2x + 7)
= x2 + 3x + 2x - 2 - 5 + 7
= x2 + 5x