# At the beginning of the month, a song on a streaming service already had 1,000 listens, and was getting 38 new listens each day. Meanwhile, a different song already had 900 listens, and was getting 40 new listens each day. Write an equation to show the number of days it would take for the two songs to have the same number of listens. Use x as your variable.(1 point)

## The equation can be written as:

1000 + 38x = 900 + 40x

Where x is the number of days it takes for the two songs to have the same number of listens.

Simplifying, we get:

1000 - 900 = 40x - 38x

100 = 2x

x = 50

Therefore, it would take 50 days for the two songs to have the same number of listens.

## 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.(1 point)

Responses

10x=32−6x ; x=2
10 x equals 32 minus 6 x ; x equals 2

10x=32+6x ; x=8
10 x equals 32 plus 6 x ; x equals 8

10=32+6x ; x=−3
10 equals 32 plus 6 x ; x equals negative 3

10x=32+6x ; x=4
10 x equals 32 plus 6 x ; x equals 4

## Miguel’s car has a 20-gallon capacity, and Christina’s car has a 16-gallon capacity. Miguel uses 1.5 gallons of gas per week, and Christina uses 1 gallon of gas per week. When will Miguel and Christina have the same amount of gas in their tanks?(1 point)

Responses

After 8 weeks they will have the same amount of gas in their tanks.
After 8 weeks they will have the same amount of gas in their tanks.

After −8 weeks they will have the same amount of gas in their tanks.
After negative 8 weeks they will have the same amount of gas in their tanks.

After 18 week they will have the same amount of gas in their tanks.
After Start Fraction 1 over 8 End Fraction week they will have the same amount of gas in their tanks.

After 1.6 weeks they will have the same amount of gas in their tanks.

## negative 8 x plus 3 equals negative 8 x plus 3

−3x+8=−3x−8
negative 3 x plus 8 equals negative 3 x minus 8

−3x−8=3x−8
negative 3 x minus 8 equals 3 x minus 8

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

5(2x+2)−4=2x+6(1 point)
Responses

The equation has one solution: x=0.
The equation has one solution: x equals 0 .

The equation has one solution: x=1.
The equation has one solution: x equals 1 .

The equation has infinite solutions.
The equation has infinite solutions.

The equation has no solution.

5x+8+x=32

(4 points)

## To find the number of days it would take for the two songs to have the same number of listens, we can set up an equation based on the given information.

Let's start with the first song, which had 1,000 listens at the beginning of the month and is getting 38 new listens each day. We can express this situation with the equation:

Listens for the first song = 1,000 + 38x

Here, x represents the number of days.

Now, let's consider the second song, which had 900 listens at the beginning of the month and is getting 40 new listens each day. We can express this as:

Listens for the second song = 900 + 40x

We want to find the number of days (x) when the two songs have the same number of listens. Since we set them equal to each other, the equation becomes:

1,000 + 38x = 900 + 40x

Now, we can solve the equation to find the value of x, which represents the number of days it would take for the two songs to have the same number of listens.

## At the beginning of the month, a song on a streaming service had 700 listens, and it was getting 52 new listens each day. Meanwhile, a different song had 600 listens, and it was getting 56 new listens each day. When will the two songs have the same number of listens?(1 point)

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

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

11x=3(7x−1)−10x(1 point)
Responses

The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .

The equation has one solution: x=−1.
The equation has one solution: x equals negative 1 .

The equation has no solution.
The equation has no solution.

The equation has infinite solutions.
The equation has infinite solutions.