To solve the equation 2x - 3 = x + 1, we need to isolate the variable x on one side of the equation.

First, let's simplify both sides of the equation by combining like terms:

2x - 3 = x + 1

To eliminate the x term on the right side, we can subtract x from both sides:

2x - x - 3 = x - x + 1

This simplifies to:

x - 3 = 1

Next, let's isolate the x term by adding 3 to both sides:

x - 3 + 3 = 1 + 3

This simplifies to:

x = 4

Therefore, the solution to the equation 2x - 3 = x + 1 is x = 4.