Question

1. 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, ((x^2 - 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? (1 point)

(x^2 - x)
(x^2 + 5x + 14)
(x^2 + 5x)
(x^2 - x + 14)

Explanation:

Step1: Sum all distance expressions

$(3x - 2) + (x^2 - 5) + (2x + 7)$

Step2: Group like terms

$x^2 + (3x + 2x) + (-2 - 5 + 7)$

Step3: Simplify each term group

$x^2 + 5x + 0$

Answer:

$x^2 + 5x$ (corresponding to the third option)