Amanda's family is taking a road trip. Their car can travel no more than 352 miles without needing to refill the gas tank. They have traveled 108 miles since they last filled the gas tank. Amanda knows that the inequality representing this situation is 108+x≤352.

Select from the drop-down menu to correctly interpret the solution of this inequality.
Amanda's family can drive miles before they need to refill the gas tank.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

2y+y=5

add 2y and y