To solve the equation \(5x - 2 = 3x + 4\), we need to isolate the variable \(x\). Let's go through the steps:

1. **Move all terms involving \(x\) to one side:**

   Start by subtracting \(3x\) from both sides to get all \(x\)-terms on one side of the equation:

   \[
   5x - 3x - 2 = 3x - 3x + 4
   \]

   Simplifying this gives:

   \[
   2x - 2 = 4
   \]

2. **Move constant terms to the other side:**

   Next, add \(2\) to both sides to isolate the terms with \(x\):

   \[
   2x - 2 + 2 = 4 + 2
   \]

   Simplifying this gives:

   \[
   2x = 6
   \]

3. **Solve for \(x\):**

   Divide both sides by \(2\) to solve for \(x\):

   \[
   x = \frac{6}{2}
   \]

   Simplifying this gives:

   \[
   x = 3
   \]

So, the solution to the equation is \(x = 3\).

Would you like further details or have any questions about this solution? Here are some related questions you might find interesting:

1. What would the solution be if the equation was \(5x - 2 = 3x - 4\)?
2. How would the steps change if the equation had a different variable, such as \(5y - 2 = 3y + 4\)?
3. What happens if we have equations with more than one variable?
4. How do we check if our solution is correct?
5. What are some strategies for solving more complex linear equations?

**Tip:** Always perform the same operation on both sides of an equation to maintain equality.

Learn how to solve the equation 5x - 2 = 3x + 4 with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations and isolating variables. Suitable for students in Grades 7-9.

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