Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
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.
1.Write an equation to model the number of movies m you have to watch before you earn a free movie pass.
2.Solve the equation. Show your work.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Julia is allowed to watch no more than 5 hours of television a week. So far this week, she has watched 1.5 hours. Write and solve an inequality to show how many hours of television Julia can still watch this week.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
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.
please give the answers
40 + 2x = 100
and
1.5 + x = 5
what is the right answer??
1. To find the number of movies m you have to watch before you earn a free movie pass, you can use the equation:
40 + 2m = 100
First, subtract 40 from both sides of the equation:
40 + 2m - 40 = 100 - 40
2m = 60
Then, divide both sides of the equation by 2:
2m/2 = 60/2
m = 30
So, you have to watch 30 movies before you earn a free movie pass.
2. To show how many hours of television Julia can still watch this week, you can use the inequality:
1.5 + x ≤ 5
Here, x represents the additional hours of television Julia can still watch.
To solve the inequality, subtract 1.5 from both sides:
1.5 + x - 1.5 ≤ 5 - 1.5
x ≤ 3.5
Julia can still watch up to 3.5 more hours of television this week.
3. An example of an equation with a variable on both sides and infinitely many solutions is:
2x - 3 = 2x + 1
To solve this equation, you can subtract 2x from both sides:
2x - 3 - 2x = 2x + 1 - 2x
-3 = 1
This equation is contradictory. It states that -3 is equal to 1, which is not possible. Therefore, the equation has no solution.
Since the equation has no solution, every value of x will make the equation false. Therefore, it has infinitely many solutions.
1. To find the equation that models the number of movies m you have to watch before earning a free movie pass, we can use the following information:
- You earn 2 advantage points for every movie you see.
- When you earn 100 points, you get a free movie pass.
- Currently, you have 40 advantage points.
The equation can be written as:
2m + 40 = 100
To solve the equation:
1. Subtract 40 from both sides: 2m = 60
2. Divide both sides by 2: m = 30
Therefore, you need to watch 30 more movies to earn a free movie pass.
2. To write and solve an inequality to show how many hours of television Julia can still watch this week, we can use the following information:
- Julia is allowed to watch no more than 5 hours of television a week.
- So far, this week, she has watched 1.5 hours.
Let x represent the number of hours Julia can still watch this week. The inequality can be written as:
1.5 + x ≤ 5
To solve the inequality:
1. Subtract 1.5 from both sides: x ≤ 5 - 1.5
2. Simplify: x ≤ 3.5
Therefore, Julia can still watch up to 3.5 hours of television this week.
3. Writing an equation with a variable on both sides of the equal sign that has infinitely many solutions can be done by equating the same expression or variable on both sides. For example:
2x + 5 = 2x + 10
To solve the equation:
1. Subtract 2x from both sides: 5 = 10
The equation simplifies to 5 = 10, which is not true. However, since both sides of the equation contain the same variable (x) and it got cancelled out during the simplification process, it means that any value of x will satisfy this equation. Therefore, this equation has an infinite number of solutions.