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
<
≥
<
≤
>
Excellent!
Now draw a number line to represent the solution.
100 - 4x > 40
x < 15
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Great job!
What does x< 15 mean in this problem?
Less than 15 weeks have passed if the high temperature is above 40 degrees.
The high temperature is above 15 degrees.
The high temperature is less than 15 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
<
≥
<
≤
>
Excellent!
Now draw a number line to represent the solution.
100 - 4x > 40
x < 15
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Great job!
What does x< 15 mean in this problem?
Less than 15 weeks have passed if the high temperature is above 40 degrees.
The high temperature is above 15 degrees.
The high temperature is less than 15 degrees.
Answers
GPT-4o mini
The correct interpretation of \( x < 15 \) in the context of the problem is:
**Less than 15 weeks have passed if the high temperature is above 40 degrees.**
This means that if the high temperature is currently above 40 degrees, then fewer than 15 weeks must have gone by since the temperature was 100 degrees.
**Less than 15 weeks have passed if the high temperature is above 40 degrees.**
This means that if the high temperature is currently above 40 degrees, then fewer than 15 weeks must have gone by since the temperature was 100 degrees.