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
≤
≥
<
>
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
≤
≥
<
>
Answers
GPT-4o mini
To complete the statement representing the solution to the inequality, we need to determine whether \( x \) (the number of minutes) can be less than or equal to the boundary, or greater than the boundary.
From the analysis, we found:
- For \( x = 5 \): the inequality \( 100 - 6(5) < 64 \) evaluates to \( 70 < 64 \), which is **false**.
- For \( x = 6 \): the inequality \( 100 - 6(6) < 64 \) evaluates to \( 64 < 64 \), which is **false** as well.
- For \( x = 7 \): the inequality \( 100 - 6(7) < 64 \) evaluates to \( 58 < 64 \), which is **true**.
Since the values of \( x \) less than or equal to 6 do not satisfy the inequality, while values greater than 6 do, we can conclude that the solution to the inequality is:
\[ x > 6 \]
Thus, we can fill in the statement as follows:
\[ x \, > \, 6 \]
From the analysis, we found:
- For \( x = 5 \): the inequality \( 100 - 6(5) < 64 \) evaluates to \( 70 < 64 \), which is **false**.
- For \( x = 6 \): the inequality \( 100 - 6(6) < 64 \) evaluates to \( 64 < 64 \), which is **false** as well.
- For \( x = 7 \): the inequality \( 100 - 6(7) < 64 \) evaluates to \( 58 < 64 \), which is **true**.
Since the values of \( x \) less than or equal to 6 do not satisfy the inequality, while values greater than 6 do, we can conclude that the solution to the inequality is:
\[ x > 6 \]
Thus, we can fill in the statement as follows:
\[ x \, > \, 6 \]