Question
Sarah is hiking. She starts at 80 feet and hikes up at a constant rate of 4 feet per minute. How many minutes could she be hiking if she is above 270 feet in elevation?
Write an inequality to represent the situation. Use x to represent the number of minutes.
80+4x>270
Good work!
You just wrote an inequality to represent the situation. Now solve the associated equation, 80 + 4x = 270, to find the boundary for the inequality. Show your work or solve on paper.
80 + 4x > 270
80+4x
=
270
x
=
47.5
Nice!
Now figure out if the boundary, x = 47.5, is a solution to the inequality. Does x = 47.5 make the inequality true or false?
80 + 4x > 270
True
False
Write an inequality to represent the situation. Use x to represent the number of minutes.
80+4x>270
Good work!
You just wrote an inequality to represent the situation. Now solve the associated equation, 80 + 4x = 270, to find the boundary for the inequality. Show your work or solve on paper.
80 + 4x > 270
80+4x
=
270
x
=
47.5
Nice!
Now figure out if the boundary, x = 47.5, is a solution to the inequality. Does x = 47.5 make the inequality true or false?
80 + 4x > 270
True
False
Answers
GPT-4o mini
To determine if the boundary \( x = 47.5 \) is a solution to the inequality \( 80 + 4x > 270 \), we substitute \( x \) with \( 47.5 \) in the inequality:
\[
80 + 4(47.5) > 270
\]
Calculating \( 4(47.5) \):
\[
80 + 190 > 270
\]
Now simplify the left side:
\[
270 > 270
\]
This statement is **false** because \( 270 \) is not greater than \( 270 \); they are equal. Therefore, the boundary \( x = 47.5 \) does not satisfy the inequality \( 80 + 4x > 270 \).
So, the answer is:
**False**.
\[
80 + 4(47.5) > 270
\]
Calculating \( 4(47.5) \):
\[
80 + 190 > 270
\]
Now simplify the left side:
\[
270 > 270
\]
This statement is **false** because \( 270 \) is not greater than \( 270 \); they are equal. Therefore, the boundary \( x = 47.5 \) does not satisfy the inequality \( 80 + 4x > 270 \).
So, the answer is:
**False**.