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 $560?
Write an inequality to represent the situation. Use x to represent the number of days.
60x+20≤560
Great job!
You just wrote an inequality to represent the situation. Now solve the associated equation, 20 + 60x = 560, to find the boundary for the inequality. Show your work or solve on paper.
20 + 60x ≤ 560
20+60x
=
560
x
=
9
Good work!
You found that x = 9 is the solution to the associated equation. Is x = 9 also included in the solutions to the inequality?
20 + 60x ≤ 560
Yes
No
You got it!
You found that x = 9 is included in the solutions. In other words, x = 9 makes the inequality true. Now test a value below the boundary, x = 8, and a value above the boundary, x = 10. Do they make the inequality true or false?
x= 8x=9 (boundary)x= 1020 + 60x ≤ 560
True
False
True
True
False
True
False
Nice!
Complete the statement so that it represents the solution to the inequality. Use the table to help you.
x= 8x=9 (boundary)x= 1020 + 60x ≤ 560TrueTrueFalse
x
≤
<
≥
>
≤
Good work!
Draw a number line to represent the solution.
20 + 60x ≤ 560
x ≤ 9
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Nice!
What does x≤ 9 mean in this problem?
The car can be rented for 9 or fewer days.
The price per day can be $9 or less.
The car can be rented for 9 or more days.
Write an inequality to represent the situation. Use x to represent the number of days.
60x+20≤560
Great job!
You just wrote an inequality to represent the situation. Now solve the associated equation, 20 + 60x = 560, to find the boundary for the inequality. Show your work or solve on paper.
20 + 60x ≤ 560
20+60x
=
560
x
=
9
Good work!
You found that x = 9 is the solution to the associated equation. Is x = 9 also included in the solutions to the inequality?
20 + 60x ≤ 560
Yes
No
You got it!
You found that x = 9 is included in the solutions. In other words, x = 9 makes the inequality true. Now test a value below the boundary, x = 8, and a value above the boundary, x = 10. Do they make the inequality true or false?
x= 8x=9 (boundary)x= 1020 + 60x ≤ 560
True
False
True
True
False
True
False
Nice!
Complete the statement so that it represents the solution to the inequality. Use the table to help you.
x= 8x=9 (boundary)x= 1020 + 60x ≤ 560TrueTrueFalse
x
≤
<
≥
>
≤
Good work!
Draw a number line to represent the solution.
20 + 60x ≤ 560
x ≤ 9
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Nice!
What does x≤ 9 mean in this problem?
The car can be rented for 9 or fewer days.
The price per day can be $9 or less.
The car can be rented for 9 or more days.
Answers
GPT-4o mini
The correct interpretation of \( x \leq 9 \) in this problem is:
**The car can be rented for 9 or fewer days.**
This means that the maximum number of days for which the car can be rented without exceeding the total cost of $560 is 9 days.
**The car can be rented for 9 or fewer days.**
This means that the maximum number of days for which the car can be rented without exceeding the total cost of $560 is 9 days.