Question

Emily worked out for more than 25 minutes total. She spent 10 minutes running, and x minutes each on 2 stations. How much time could she have spent on each station?
Write an inequality to represent the situation. Use x to represent the minutes spent on each of the stations.

10+2x>25
Nice!
You just wrote an inequality to represent the situation. Now solve the associated equation, 10 + 2x = 25, to find the boundary for the inequality. Show your work or solve on paper.

10 + 2x > 25
10+2x
=
25

x
=

7.5
Excellent!
You found that x = 7.5 is the solution to the associated equation and the boundary of the inequality. Does the boundary, x = 7.5, make the inequality true or false?
x= 7 x=7.5 (boundary) x= 8
10 + 2x > 25 ?


True
False
?

Answer 1

To check whether the boundary \( x = 7.5 \) makes the inequality \( 10 + 2x > 25 \) true or false, we substitute \( x = 7.5 \) into the inequality.

1. Substitute \( x = 7.5 \) into the left side of the inequality:
\[
10 + 2(7.5) = 10 + 15 = 25
\]

2. Now we compare:
\[
25 > 25
\]

Since \( 25 \) is not greater than \( 25 \), this means that \( x = 7.5 \) does not make the inequality true—it's actually the boundary point.

Now let's check \( x = 7 \) and \( x = 8 \):

- For \( x = 7 \):
\[
10 + 2(7) = 10 + 14 = 24
\]
So, \( 24 > 25 \) is **False**.

- For \( x = 8 \):
\[
10 + 2(8) = 10 + 16 = 26
\]
So, \( 26 > 25 \) is **True**.

Thus:
- For \( x = 7 \): **False**
- For \( x = 7.5 \) (boundary): **False**
- For \( x = 8 \): **True**