Question

henry is driving his car on a business trip. he knows he will drive for at least 120 kilometers on the trip. also, he will drive for at most 165 kilometers on the trip (so that his company can cover his gas expenses). he has 5 days left on the trip. let x be the number of kilometers per day he will drive for those 5 days. (suppose he will decide to drive the same distance each day.) he has already driven the car for 60 kilometers on the trip.
(a) find the possible numbers of kilometers per day he 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 he will drive.

Explanation:

Step1: Define total distance range

Let total distance = $60 + 5x$.
Minimum total: $60 + 5x \geq 120$
Maximum total: $60 + 5x \leq 165$

Step2: Solve lower bound inequality

Subtract 60 from both sides:
$5x \geq 120 - 60$
$5x \geq 60$
Divide by 5:
$x \geq 12$

Step3: Solve upper bound inequality

Subtract 60 from both sides:
$5x \leq 165 - 60$
$5x \leq 105$
Divide by 5:
$x \leq 21$

Step4: Combine inequalities

Combine the two results into a compound inequality.

Answer:

(a) $12 \leq x \leq 21$
(b) On the number line:

• Plot a closed dot at 12 and a closed dot at 21.
• Draw a solid line segment connecting the two dots to represent all values between 12 and 21, inclusive.