Question

The cost of renting a car is $60 per day plus a one-time fee of $20 for insurance. How many days can the car be rented if the total cost is to be no more than $440?
Write an inequality to represent the situation. Use x to represent the number of days.

20+60x≤440
Nice!
You just wrote an inequality to represent the situation. Now solve the associated equation, 20 + 60x = 440, to find the boundary for the inequality. Show your work or solve on paper.

20 + 60x ≤ 440
20+60x
=
440

x
=

7
You got it!
You found that x = 7 is the solution to the associated equation. Is x = 7 also included in the solutions to the inequality?
20 + 60x ≤ 440

Yes

No
Great job!
You found that x = 7 is included in the solutions. In other words, x = 7 makes the inequality true. Now test a value below the boundary, x = 6, and a value above the boundary, x = 8. Do they make the inequality true or false?

x= 6 x=7 (boundary) x= 8
20 + 60x ≤ 440

True
True
False
True

False
True
False
Excellent!
Complete the statement so that it represents the solution to the inequality. Use the table to help you.
x= 6 x=7 (boundary) x= 8
20 + 60x ≤ 440 True True False
x

≤
≤
<
>
≥

Excellent!
Draw a number line to represent the solution.
20 + 60x ≤ 440

x ≤ 7
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14

Good work!
What does x≤ 7 mean in this problem?

The car can be rented for 7 or fewer days.

The price per day can be $7 or less.

The car can be rented for 7 or more days.

Answer 1

The correct interpretation of \( x \leq 7 \) in this problem is:

**The car can be rented for 7 or fewer days.**

This means that the maximum number of days for which the car can be rented without exceeding the total cost of $440 is 7 days.