Question

heather is planning to run a marathon. as part of her training this week, she will run at least 41 kilometers and to avoid overtraining, at most 47 kilometers. she has already run 11 kilometers in training this week. let x be the number of kilometers per session she will run for the remaining 2 training sessions this week. (suppose she will decide to run the same distance each session.) (a) find the possible numbers of kilometers per session heather 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 total distance inequality

Let total distance be $11 + 2x$. We know $41 \leq 11 + 2x \leq 47$.

Step2: Subtract 11 from all parts

Subtract 11 to isolate the term with $x$:
$41 - 11 \leq 2x \leq 47 - 11$
$30 \leq 2x \leq 36$

Step3: Divide all parts by 2

Solve for $x$ by dividing by 2:
$\frac{30}{2} \leq x \leq \frac{36}{2}$
$15 \leq x \leq 18$

Step4: Graph the compound inequality

On the number line, plot closed circles at 15 and 18, then shade the region between them.

Answer:

(a) $\boldsymbol{15 \leq x \leq 18}$
(b) On the number line: Draw closed dots at 15 and 18, and shade the segment connecting these two points.