Let's solve the equation step by step:

The given equation is:

$2x + 1 = 4x - 3$

Step 1: Subtract $2x$ from both sides to move all the terms with $x$ to one side:

$2x + 1 - 2x = 4x - 3 - 2x$

This simplifies to:

$1 = 2x - 3$

Step 2: Add $3$ to both sides to isolate the $2x$ term:

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

Simplifying further:

$4 = 2x$

Step 3: Divide both sides by $2$ to solve for $x$:

$\frac{4}{2} = \frac{2x}{2}$

$x = 2$

So, the solution to the equation is:

$x = 2$

Would you like a more detailed explanation of any of the steps, or have any questions on this?

Here are some related questions you might find interesting:

1. What happens if the equation is quadratic instead of linear?
2. How can we check the solution of an equation?
3. What are some techniques for solving equations involving fractions?
4. How do we solve inequalities, and what’s the difference from equations?
5. What is the process for solving systems of equations?

Tip: To check if your solution is correct, substitute $x = 2$ back into the original equation. If both sides are equal, you've found the correct solution!