Hi. Check my answers? Thanks? Also, if I got any wrong, explain to me why because inequalities confuse me sometimes
1. Julia is allowed to watch no more then 5 hours of tv a week. She has already watched 1.5 hours. Write and solve an inequality to show how many hours of television Julia can still watch this week.
T<5
T - 1.5 < 5 - 1.5
T = 3.5
(I know the answer's correct, but is the way I wrote it correct?)
2. You are a member of your local movie theater’s club. Every time you see a movie at the theater, you earn 2 advantage points. When you earn 100 points, you get a free movie pass. Currently, you have 40 advantage points.
A. Write an equation to model the number of movies, m, you have to watch before you earn a free movie pass.
B. Solve the equation. Show your work.
40 + 2m = 100
40 + 2m - 40 = 100 - 40
2m = 60
2m ÷ 2 = 60 ÷ 2
m = 30 movies
(Same here, I know the answer's correct, but is the way I wrote it correct?)
3. Write an equation with a variable on both sides of the equal sign that has infinitely many solutions. Solve the equation and explain why it has an infinite number of solutions.
x = x
Whatever value is on the right must match the one on the left. The equation is true regardless of the value of x.
(This one I'm not so sure it's correct)
Looks good to me.
Awesome, thank you so much!
Welcome
1. The way you wrote it is correct. You start by setting up the inequality T < 5, where T represents the number of hours Julia can still watch. Then, you subtract 1.5 from both sides to account for the time already watched, giving you T - 1.5 < 5 - 1.5. Finally, by solving for T, you find that T = 3.5. This means that Julia can still watch 3.5 hours of television this week.
2. The way you wrote it is correct. In this scenario, you earn 2 advantage points for each movie watched, and you need to earn a total of 100 points to get a free movie pass. To model the number of movies, m, you have to watch before you earn a free movie pass, you can set up the equation 40 + 2m = 100. This equation represents the current advantage points (40) plus the points earned from watching movies (2m), and it should equal 100 for you to get the free pass. By solving this equation, you find that m = 30 movies. Therefore, you will need to watch 30 movies to earn a free movie pass.
3. Your answer is correct. The equation x = x has infinitely many solutions. This is because no matter what value you assign to x, the equation will always be true. This equation essentially states that whatever value is on the right (x) must match the one on the left (also x). Since both sides are always equal, there are an infinite number of possible solutions.