An ice skating rink has two ways you can use the facility. The first option is to pay $10 per visit. The second option is to pay $32 per month, and $6 per visit. Write and solve an equation to show the number of visits it would take for the cost of the two plans to be equal.

Question

The songs will have the same number of listens after __ days

Answer 1

Let x represent the number of visits.

Cost of first option: 10x
Cost of second option: 32 + 6x

Setting these two equations equal to each other:
10x = 32 + 6x
4x = 32
x = 8

It would take 8 visits for the cost of the two plans to be equal.

Answer 2

Which of the following equations has no solutions?
A. 6x + 3 = -6x + 3
B. - 6x + 4 = 6x + 3
C. -6x + 4 = 6x + 3
D. 6x + 4 = 6x + 4

Answer 3

The equation that has no solutions is option C:

C. -6x + 4 = 6x + 3

This equation simplifies to:
-6x + 4 = 6x + 3
-6x = 6x - 1
-12x = -1
x = 1/12

Since x does not satisfy the original equation, there are no solutions.

Answer 4

Solve for x to determine if the equation has one, none, or infinite solutions.
11x = 3(7x - 1) - 10x
A. The equation has no solution
B. The equation has one solution: x = -3
C. The equations has infinite solution
D. The equations has one solution: x = -1

Answer 5

Let's simplify the equation:

11x = 3(7x - 1) - 10x
11x = 21x - 3 - 10x
11x = 11x - 3
0 = -3

The equation simplifies to 0 = -3, which is not a valid statement.

Therefore, the equation has no solution.
A. The equation has no solution.

Answer 6

Solve for x to determine if the equation has one, none, or infinite solutions.

5(2x + 2) - 4 = 2x + 6
A. The equation has no solution
B. The equation has one solution x = 1
C. The equation has infinite solutions
D. The equation has one solution x = 0

Answer 7

Let's simplify the equation step by step:

5(2x + 2) - 4 = 2x + 6
10x + 10 - 4 = 2x + 6
10x + 6 = 2x + 6
10x - 2x = 6 - 6
8x = 0
x = 0

Therefore, the equation has one solution, x = 0.
D. The equation has one solution x = 0.

Answer 8

Solve the following linear equations for x. Then check your answer. Show all your steps for solving and checking
5x + 8 + x = 32

Answer 9

To solve the equation 5x + 8 + x = 32, we will follow the steps below:

Combine like terms on the left side:
5x + 8 + x = 32
6x + 8 = 32

Subtract 8 from both sides to isolate x:
6x + 8 - 8 = 32 - 8
6x = 24

Divide by 6 on both sides to solve for x:
6x/6 = 24/6
x = 4

Now, to check our answer:
5(4) + 8 + 4 = 32
20 + 8 + 4 = 32
32 = 32

Since both sides of the equation are equal when x = 4, our solution is correct. The solution to the equation is x = 4.