Question

ali is driving his car on a business trip. he knows he will drive for at least 110 kilometers on the trip. also, he will drive for at most 150 kilometers on the trip (so that his company can cover his gas expenses). he has 4 days left on the trip. let x be the number of kilometers per day he will drive for those 4 days. (suppose he will decide to drive the same distance each day.) he has already driven the car for 70 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.

Explanation:

Step1: Define total distance range

Let total distance be $D$, so $110 \leq D \leq 150$

Step2: Set total distance equation

Total distance = driven + 4 days' driving: $D = 70 + 4x$

Step3: Substitute into lower bound

$110 \leq 70 + 4x$
$110 - 70 \leq 4x$
$40 \leq 4x$
$\frac{40}{4} \leq x$
$10 \leq x$

Step4: Substitute into upper bound

$70 + 4x \leq 150$
$4x \leq 150 - 70$
$4x \leq 80$
$x \leq \frac{80}{4}$
$x \leq 20$

Step5: Combine inequalities

Combine the two results for $x$

Answer:

$10 \leq x \leq 20$