Question

rita is driving her car on a business trip. she knows she will drive for at least 106 kilometers on the trip. also, she will drive for at most 130 kilometers on the trip (so that her company can cover her gas expenses). she has 4 days left on the trip. let x be the number of kilometers per day she will drive for those 4 days. (suppose she will decide to drive the same distance each day.) she has already driven the car for 50 kilometers on the trip.
(a) find the possible numbers of kilometers per day she will drive. 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 day she will drive.

Explanation:

Step1: Define total distance range

Let total distance be $D$. We know $106 \leq D \leq 130$.

Step2: Calculate remaining distance range

Subtract already driven 50 km:
$106 - 50 \leq 4x \leq 130 - 50$
$56 \leq 4x \leq 80$

Step3: Solve for x (divide by 4)

$\frac{56}{4} \leq x \leq \frac{80}{4}$
$14 \leq x \leq 20$

Step4: Prepare number line graph

Mark closed dots at 14 and 20, shade the segment between them.

Answer:

(a) $\boldsymbol{14 \leq x \leq 20}$
(b) On the number line:

• Place a closed (filled) dot at 14 and a closed (filled) dot at 20.
• Draw a solid line segment connecting these two dots to represent all values between 14 and 20, inclusive.