Question

rachel is planning to run a marathon. as part of her training this week, she will run at least 53 kilometers and has to avoid over - training, at most 73 kilometers. she has already run 13 kilometers in training this week. let x be the number of kilometers per session she will run for the remaining 4 training sessions this week. (a) find the possible numbers of kilometers per session rachel will run. write your answer as a compound inequality solved for x. (b) on the number line below, graph the solution that represents the possible numbers of kilometers per session she will run.

Explanation:

Step1: Set up inequalities

She will run at least 53 kilometers and has already run 13 kilometers, and will run for 4 remaining sessions with $x$ kilometers per - session. So the total distance she will run is $13 + 4x$. The inequality for the lower - bound is $13+4x\geq53$. Also, she needs to avoid overtraining, so the total distance $13 + 4x\leq73$.

Step2: Solve the first inequality

Solve $13 + 4x\geq53$. Subtract 13 from both sides: $4x\geq53 - 13$, $4x\geq40$. Then divide both sides by 4: $x\geq10$.

Step3: Solve the second inequality

Solve $13 + 4x\leq73$. Subtract 13 from both sides: $4x\leq73 - 13$, $4x\leq60$. Then divide both sides by 4: $x\leq15$.

Answer:

$10\leq x\leq15$; On the number - line, mark a closed circle at 10 and a closed circle at 15, and shade the region between them.