Question

it takes her 5 minutes to complete a lap. she will ride for more than 35 minutes. lets look at the possible numbers of laps ivanna will ride.
(a) fill in the blanks to write an inequality that can be used to find x, the number of laps ivanna will ride. choose only from (5 + x, 5 - x, x - 5, 5x, \frac{5}{x}, \frac{x}{5}, <, leq, >, geq), or 35.
inequality: (square) (square) (square)
(b) find the possible numbers of laps ivanna will ride. write your answer as an inequality solved for x.
(c) on the number line below, graph the solution that represents the possible numbers of laps ivanna will ride.

Explanation:

Step1: Define total ride time

Total time = $5x$ (5 min per lap × $x$ laps)

Step2: Set up inequality

Total time > 35 minutes, so $5x > 35$

Step3: Solve for x

Divide both sides by 5: $\frac{5x}{5} > \frac{35}{5}$ → $x > 7$

Step4: Graph the solution

On a number line, draw an open circle at 7, then shade all values to the right of 7 (since $x$ must be greater than 7, not equal to it).

Answer:

(a) Inequality: $\boldsymbol{5x > 35}$
(b) $\boldsymbol{x > 7}$
(c) On the number line: Place an open circle at 7, and draw a shaded arrow extending to the right from 7.