How do we solve the equation 11n + 1 = 35 + 3n?

To solve the equation 11n + 1 = 35 + 3n, we will follow these steps:

1. Start by isolating the variable terms on one side:

First, we want to get all the terms involving n on one side of the equation and the constants on the other side. We can do this by subtracting 3n from both sides:

11n + 1 – 3n = 35 + 3n – 3n

This simplifies to:

8n + 1 = 35

2. Next, move the constant to the other side:

Now we need to eliminate the constant on the left side by subtracting 1 from both sides:

8n + 1 – 1 = 35 – 1

This simplifies to:

8n = 34

3. Finally, solve for n:

To isolate n, divide both sides of the equation by 8:

n = 34 / 8

When we simplify this fraction, we get:

n = 4.25

In conclusion, the solution to the equation 11n + 1 = 35 + 3n is n = 4.25.