Question
The high temperature outside one day is 100 degrees. The high temperature decreases at a constant rate of 4 degrees per week. How many weeks could have passed if the high temperature is now above 40 degrees?
Write an inequality to represent the situation. Use x to represent the number of weeks.
100−4x>40
Nice!
You just wrote an inequality to represent the situation. Now solve the associated equation, 100 - 4x = 40, to find the boundary for the inequality. Show your work or solve on paper.
100 - 4x > 40
100−4x
=
40
x
=
15
Good work!
You found that x = 15 is the solution to the associated equation and the boundary of the inequality. Does the boundary, x = 15, make the inequality true or false?
x= 14 x=15 (boundary) x= 16
100 - 4x > 40 ?
False
True
False
?
Nice!
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= 14 x=15 (boundary) x= 16
100 - 4x > 40
True
True
False
False
False
False
True
Great job!
Complete the statement so that it represents the solution to the inequality. You can use the table to help you.
x= 14 x=15 (boundary) x= 16
100 - 4x > 40 True False False
x
≥
<
≤
>
Write an inequality to represent the situation. Use x to represent the number of weeks.
100−4x>40
Nice!
You just wrote an inequality to represent the situation. Now solve the associated equation, 100 - 4x = 40, to find the boundary for the inequality. Show your work or solve on paper.
100 - 4x > 40
100−4x
=
40
x
=
15
Good work!
You found that x = 15 is the solution to the associated equation and the boundary of the inequality. Does the boundary, x = 15, make the inequality true or false?
x= 14 x=15 (boundary) x= 16
100 - 4x > 40 ?
False
True
False
?
Nice!
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= 14 x=15 (boundary) x= 16
100 - 4x > 40
True
True
False
False
False
False
True
Great job!
Complete the statement so that it represents the solution to the inequality. You can use the table to help you.
x= 14 x=15 (boundary) x= 16
100 - 4x > 40 True False False
x
≥
<
≤
>
Answers
GPT-4o mini
To complete the statement that represents the solution to the inequality \(100 - 4x > 40\), we can analyze the table you've provided and the results of our boundary check.
From your findings:
- For \(x = 14\), the inequality \(100 - 4(14) > 40\) holds true, so this value satisfies the inequality.
- For \(x = 15\), the inequality \(100 - 4(15) > 40\) is false, meaning this value does not satisfy the inequality.
- For \(x = 16\), the inequality \(100 - 4(16) > 40\) is also false, meaning this value does not satisfy the inequality.
Since \(x = 14\) makes the inequality true and \(x = 15\) (the boundary) does not, the correct statement indicating the solution to the inequality would be that \(x\) is less than the boundary:
So the final statement is:
\[
x < 15
\]
or equivalently as the solution to the inequality:
\[
x \leq 14
\]
Thus the completed solution is \(x < 15\).
From your findings:
- For \(x = 14\), the inequality \(100 - 4(14) > 40\) holds true, so this value satisfies the inequality.
- For \(x = 15\), the inequality \(100 - 4(15) > 40\) is false, meaning this value does not satisfy the inequality.
- For \(x = 16\), the inequality \(100 - 4(16) > 40\) is also false, meaning this value does not satisfy the inequality.
Since \(x = 14\) makes the inequality true and \(x = 15\) (the boundary) does not, the correct statement indicating the solution to the inequality would be that \(x\) is less than the boundary:
So the final statement is:
\[
x < 15
\]
or equivalently as the solution to the inequality:
\[
x \leq 14
\]
Thus the completed solution is \(x < 15\).