Question

Solve for x: 12x + 5 = 10x -11.
(1 point)
Х =

Answer 1

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.

Answer 2

Answer

Answer 3

To solve the equation \( 12x + 5 = 10x - 11 \), follow these steps:

1. Subtract \( 10x \) from both sides:
\[
12x - 10x + 5 = -11
\]
This simplifies to:
\[
2x + 5 = -11
\]

2. Subtract 5 from both sides:
\[
2x = -11 - 5
\]
This simplifies to:
\[
2x = -16
\]

3. Divide both sides by 2:
\[
x = \frac{-16}{2}
\]
This simplifies to:
\[
x = -8
\]

Thus, the solution is:
\[
\boxed{-8}
\]

Answer 4

Let \( x \) be the number of days. We can set up equations for the total number of listens for each song over time.

For the first song:
- Initial listens: 1,000
- New listens per day: 38
- Total listens after \( x \) days:
\[
1000 + 38x
\]

For the second song:
- Initial listens: 900
- New listens per day: 40
- Total listens after \( x \) days:
\[
900 + 40x
\]

We want to find the number of days when the listens for both songs are equal, so we set the two equations equal to each other:
\[
1000 + 38x = 900 + 40x
\]

This is the equation that shows the number of days it would take for the two songs to have the same number of listens.

Answer 5

To solve the equation \(1000 + 38x = 900 + 40x\), we'll first simplify and isolate \(x\):

1. Start by subtracting \(38x\) from both sides:
\[
1000 = 900 + 2x
\]

2. Next, subtract \(900\) from both sides:
\[
100 = 2x
\]

3. Now, divide both sides by \(2\):
\[
x = 50
\]

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