Question

eric is planning to run a marathon. as part of his training this week, he will run more than 53 kilometers and to avoid overtraining, less than 73 kilometers. he has already run 13 kilometers in training this week. let x be the number of kilometers per session he will run for the remaining 4 training sessions this week. (suppose he will decide to run the same distance each session.) (a) find the possible numbers of kilometers per session eric 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 he will run.

Explanation:

Step1: Set up total distance inequality

$53 < 13 + 4x < 73$

Step2: Subtract 13 from all parts

$53 - 13 < 13 + 4x - 13 < 73 - 13$
$40 < 4x < 60$

Step3: Divide all parts by 4

$\frac{40}{4} < \frac{4x}{4} < \frac{60}{4}$
$10 < x < 15$

Step4: Explain number line graph

The solution $10 < x < 15$ means we mark an open circle at 10 (since $x$ is greater than 10, not equal) and an open circle at 15 (since $x$ is less than 15, not equal), then shade the region between these two points on the number line.

Answer:

(a) $10 < x < 15$
(b) On the number line: draw an open circle at 10, an open circle at 15, and shade the segment between these two points.