Question
A small kiddie pool starts with 100 gallons of water. The pool is being drained at a constant rate of 6 gallons per minute. How many minutes could have passed if the pool now has less than 64 gallons of water left?
Write an inequality to represent the situation. Use x to represent the number of minutes.
100−6x<64
Excellent!
You just wrote an inequality to represent the situation. Now solve the associated equation, 100 - 6x = 64, to find the boundary for the inequality. Show your work or solve on paper.
100 - 6x < 64
100−6x
=
64
x
=
6
You got it!
You found that x = 6 is the solution to the associated equation and the boundary of the inequality. Does the boundary, x = 6, make the inequality true or false?
x= 5x=6 (boundary)x= 7100 - 6x < 64?
False
True
False
?
Good work!
You found the boundary made the inequality false. Fill in the table to show whether a value below the boundary and a value above the boundary make the inequality true or false.
x= 5x=6 (boundary)x= 7100 - 6x < 64
False
True
False
False
True
True
False
Nice!
Complete the statement so that it represents the solution to the inequality. You can use the table to help you.
x= 5x=6 (boundary)x= 7100 - 6x < 64FalseFalseTrue
x
>
≤
≥
<
>
Excellent!
Draw a number line to represent the solution.
100 - 6x < 64
x > 6
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
You got it!
What does x> 6 mean in this problem?
More than 6 minutes have passed if there are less than 64 gallons water in the pool.
There are more than 6 gallons of water in the pool.
There are less than 6 gallons of water in the pool.
Write an inequality to represent the situation. Use x to represent the number of minutes.
100−6x<64
Excellent!
You just wrote an inequality to represent the situation. Now solve the associated equation, 100 - 6x = 64, to find the boundary for the inequality. Show your work or solve on paper.
100 - 6x < 64
100−6x
=
64
x
=
6
You got it!
You found that x = 6 is the solution to the associated equation and the boundary of the inequality. Does the boundary, x = 6, make the inequality true or false?
x= 5x=6 (boundary)x= 7100 - 6x < 64?
False
True
False
?
Good work!
You found the boundary made the inequality false. Fill in the table to show whether a value below the boundary and a value above the boundary make the inequality true or false.
x= 5x=6 (boundary)x= 7100 - 6x < 64
False
True
False
False
True
True
False
Nice!
Complete the statement so that it represents the solution to the inequality. You can use the table to help you.
x= 5x=6 (boundary)x= 7100 - 6x < 64FalseFalseTrue
x
>
≤
≥
<
>
Excellent!
Draw a number line to represent the solution.
100 - 6x < 64
x > 6
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
You got it!
What does x> 6 mean in this problem?
More than 6 minutes have passed if there are less than 64 gallons water in the pool.
There are more than 6 gallons of water in the pool.
There are less than 6 gallons of water in the pool.
Answers
GPT-4o mini
You are correct! The statement \( x > 6 \) means that more than 6 minutes have passed if there are less than 64 gallons of water left in the pool. This indicates that, after 6 minutes, the pool will have less than 64 gallons of water, and the solution \( x > 6 \) refers to the amount of time that has elapsed beyond that point.
So, the correct interpretation is:
**More than 6 minutes have passed if there are less than 64 gallons of water in the pool.**
So, the correct interpretation is:
**More than 6 minutes have passed if there are less than 64 gallons of water in the pool.**