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
False
True


True
False

Answer 1

Let's evaluate the inequality \(20 + 60x \leq 440\) for the values \(x = 6\) and \(x = 8\) to determine if they make the inequality true or false.

1. **For \(x = 6\)**:
\[
20 + 60(6) \leq 440
\]
\[
20 + 360 \leq 440
\]
\[
380 \leq 440 \quad \text{(True)}
\]

2. **For \(x = 7\)** (boundary):
\[
20 + 60(7) \leq 440
\]
\[
20 + 420 \leq 440
\]
\[
440 \leq 440 \quad \text{(True)}
\]

3. **For \(x = 8\)**:
\[
20 + 60(8) \leq 440
\]
\[
20 + 480 \leq 440
\]
\[
500 \leq 440 \quad \text{(False)}
\]

So the results are:

- **For \(x = 6\)**: True
- **For \(x = 7\)**: True
- **For \(x = 8\)**: False

This confirms that \(x = 6\) satisfies the inequality, \(x = 7\) is the boundary and satisfies the inequality, and \(x = 8\) does not satisfy the inequality.