Asked by ang3l under the stars

Solve the following equation for x. Express your answer in the simplest form.
3(-7x-6)=-2(x-6)
Answered by ang3l under the stars
what would x equal if there was only one solution?
Answered by ang3l under the stars
Solve the following equation for x. Express your answer in the simplest form.
3(x-2)=3x-7
Answered by ang3l under the stars
Autumn has a points card for a movie theater.
She receives 40 rewards points just for signing up.
She earns 12.5 points for each visit to the movie theater.
She needs at least 225 points for a free movie ticket.

Write and solve an inequality which can be used to determine vv, the number of visits Autumn can make to earn her first free movie ticket.
Answered by ang3l under the stars
what does *vv mean in your answer??
Answered by ang3l under the stars
A group of friends wants to go to the amusement park. They have no more than $295 to spend on parking and admission. Parking is $11.50, and tickets cost $39 per person, including tax. Which inequality can be used to determine xx, the maximum number of people who can go to the amusement park?
Answered by GPT 3.5
Expanding both sides of the equation, we have:
-21x - 18 = -2x + 12
Adding 2x to both sides, we get:
-19x - 18 = 12
Adding 18 to both sides, we get:
-19x = 30
Dividing both sides by -19, we find:
x = -30/19
Answered by GPT 3.5
If there is only one solution, it means that the equation has only one possible value for x. To find this value, we can continue solving the equation:

-21x - 18 = -2x + 12

Adding 2x to both sides:

-19x - 18 = 12

Adding 18 to both sides:

-19x = 30

Dividing both sides by -19:

x = -30/19

Therefore, the value of x when there is only one solution is x = -30/19.
Answered by GPT 3.5
Let's begin solving the equation step-by-step:

3(x-2) = 3x-7

First, distribute the 3 to both terms inside the parentheses:

3x - 6 = 3x - 7

Next, subtract 3x from both sides to move the variable terms to one side:

-6 = -7

Since the equation -6 = -7 is not true, this implies that there is no value of x that satisfies the equation. Therefore, there is no solution for this equation.
Answered by GPT 3.5
Let's denote vv as the number of visits Autumn can make to earn her first free movie ticket. To determine the inequality, we can use the information given in the problem.

Autumn receives 40 rewards points just for signing up and earns 12.5 points for each visit. Therefore, the total number of points Autumn will have after vv visits can be calculated as:

Total Points = 40 + 12.5*vv

Since Autumn needs at least 225 points for a free movie ticket, we can set up the following inequality:

40 + 12.5*vv ≥ 225

To solve for vv, we need to isolate the variable by subtracting 40 from both sides:

12.5*vv ≥ 225 - 40
12.5*vv ≥ 185

Finally, divide both sides by 12.5 to solve for vv:

vv ≥ 185 / 12.5
vv ≥ 14.8

Since vv represents the number of visits, and we cannot have a fraction of a visit, Autumn would need to make at least 15 visits to earn her first free movie ticket.
Answered by GPT 3.5
I apologize for the confusion caused. The * symbol represents multiplication in the equation mentioned. So, "12.5*vv" means 12.5 multiplied by vv.
Answered by GPT 3.5
To determine the maximum number of people, xx, who can go to the amusement park, we need to find the combination of parking and ticket costs that does not exceed the total budget of $295.

The cost of parking for one car is $11.50 and the cost of tickets for each person is $39. So, the total cost for xx people and one car can be represented as:

Total Cost = 11.50 + 39*xx

To ensure this total cost does not exceed the budget of $295, we can set up the following inequality:

11.50 + 39*xx ≤ 295

Therefore, the inequality that can be used to determine the maximum number of people who can go to the amusement park, xx, is:

11.50 + 39*xx ≤ 295