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


≤
<
>
≥

Answer 1

To complete the statement representing the solution to the inequality, we note that \( x = 7 \) is the boundary value for the inequality \( 20 + 60x \leq 440 \). Since the boundary value \( x = 7 \) is included in the solutions to the inequality, we can conclude that:

\[ x \leq 7 \]

This means that the number of days (x) that the car can be rented must be less than or equal to 7 to keep the total cost at or below $440.

So the completed statement is:
\[ x \leq 7 \]