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).

Let's denote the number of listens for the first song after \( x \) days as \( L_1 \) and for the second song as \( L_2 \).

For the first song:

• Initial listens = 1,000
• New listens per day = 38
• So, the total listens after \( x \) days will be: \[ L_1 = 1000 + 38x \]

For the second song:

• Initial listens = 900
• New listens per day = 40
• So, the total listens after \( x \) days will be: \[ L_2 = 900 + 40x \]

To find out when the two songs have the same number of listens, we set \( L_1 \) equal to \( L_2 \): \[ 1000 + 38x = 900 + 40x \]

This equation can be used to calculate the number of days \( x \) it will take for the two songs to have the same number of listens.

To solve the equation \(1000 + 38x = 900 + 40x\), we can follow these steps:

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

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

3. Finally, divide both sides by 2 to solve for \(x\): \[ x = 50 \]

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