Question

Ms. Jones is hiking. She starts at 40 feet and hikes up at a constant rate of 8 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.

40+8x>270

Excellent!

You just wrote an inequality to represent the situation. Now solve the associated equation, 40 + 8x = 270, to find the boundary for the inequality. Show your work or solve on paper.

40 + 8x > 270

40+8x

=

270

 

x

=

28.75

Excellent!

Now figure out if the boundary, x = 28.75, is a solution to the inequality. Does x = 28.75 make the inequality true or false?

40 + 8x > 270

True

False

Answer 1

To determine whether \( x = 28.75 \) is a solution to the inequality \( 40 + 8x > 270 \), we can substitute \( x = 28.75 \) into the left-hand side of the inequality and see if it results in a value greater than 270.

1. Substitute \( x = 28.75 \) into the expression:
\[
40 + 8(28.75) = 40 + 230 = 270
\]

2. Now we compare the result to 270:
\[
270 > 270 \quad \text{(This is false)}
\]

Since \( 270 \) is **not** greater than \( 270 \), we conclude that:

The statement \( 40 + 8(28.75) > 270 \) is **False**.

Thus, the boundary \( x = 28.75 \) itself does not satisfy the inequality \( 40 + 8x > 270 \).