Question Jessica wants to run a mile faster than 8.5 minutes. Which inequality model represents this?
Studdy Solution
STEP 1
Assumptions
1. Jessica ran a mile in 8.5 minutes yesterday.
2. Jessica wants to run a mile faster than 8.5 minutes today.
3. Let represent the time, in minutes, Jessica plans to take to run her next mile.
STEP 2
To model Jessica's goal with an inequality, we need to express that she wants to run the mile in less time than she did yesterday.
STEP 3
Since Jessica wants to run faster, the time she takes today must be less than 8.5 minutes.
STEP 4
The correct inequality to represent this situation is therefore:
STEP 5
This inequality states that the time must be less than 8.5 minutes, which aligns with Jessica's goal to beat her previous time.
STEP 6
Now, let's graph the inequality .
STEP 7
First, draw a number line representing the time in minutes.
STEP 8
Locate the point 8.5 on the number line and mark it.
STEP 9
Since the inequality is strict (), we use an open circle at 8.5 to indicate that 8.5 is not included in the solution set.
STEP 10
Draw a ray starting from the open circle at 8.5 and extending to the left, indicating all the times less than 8.5 minutes.
STEP 11
The arrow on the ray should point towards the smaller numbers, as these represent the times that are faster (less than) 8.5 minutes.
The solution to the problem is the inequality , and the graph is a number line with an open circle at 8.5 and a ray extending to the left.
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