Angela’s parents have allowed her to watch TV for a maximum of 7 hours each week. She has already watched TV for hours this week. She wants to watch some episodes of her favorite shows that are each of an hour long.
How many episodes, x, can Angela watch this week? Sketch the graph of the inequality that represents the maximum amount of episodes she can watch.
First, we need to set up an inequality to represent the situation. Angela has already watched 4 hours of TV this week, and she is allowed to watch a maximum of 7 hours. The total amount of TV time she can watch this week is given by:
Total TV time ≤ 7 hours
Total TV time = Hours already watched + Hours she can still watch
4 + x ≤ 7
x ≤ 3
Therefore, Angela can watch a maximum of 3 hours of TV this week. Since each episode is 1 hour long, she can watch a maximum of 3 episodes.
The graph of this inequality is a horizontal line at y = 3 on the x-axis. The area below this line represents the possible values for x (number of episodes) that Angela can watch.