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?
True
False
?
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?
True
False
?
Answers
GPT-4o mini
Let's evaluate the boundary \( x = 6 \) in the original inequality:
The inequality we are working with is:
\[
100 - 6x < 64
\]
Substituting \( x = 6 \) into the inequality:
\[
100 - 6(6) < 64
\]
\[
100 - 36 < 64
\]
\[
64 < 64
\]
This statement is **False** because 64 is not less than 64. Therefore, \( x = 6 \) does not satisfy the inequality.
In terms of the inequality's solution:
- \( x < 6 \) would mean that any time before 6 minutes passes makes the inequality true, so the number of minutes that could have passed is any value less than 6.
The inequality we are working with is:
\[
100 - 6x < 64
\]
Substituting \( x = 6 \) into the inequality:
\[
100 - 6(6) < 64
\]
\[
100 - 36 < 64
\]
\[
64 < 64
\]
This statement is **False** because 64 is not less than 64. Therefore, \( x = 6 \) does not satisfy the inequality.
In terms of the inequality's solution:
- \( x < 6 \) would mean that any time before 6 minutes passes makes the inequality true, so the number of minutes that could have passed is any value less than 6.