Let's solve the equation \( 5x + 1 = 3x - 2 \).

### Steps:
1. Subtract \( 3x \) from both sides to get all the \( x \)-terms on one side:
   \[
   5x - 3x + 1 = -2
   \]
   This simplifies to:
   \[
   2x + 1 = -2
   \]

2. Subtract 1 from both sides:
   \[
   2x = -2 - 1
   \]
   Simplifies to:
   \[
   2x = -3
   \]

3. Divide both sides by 2:
   \[
   x = \frac{-3}{2}
   \]
   So, \( x = -\frac{3}{2} \) or \( x = -1.5 \).

### Solution:
\( x = -1.5 \)

Would you like more details, or do you have any questions?

### Related questions:
1. How do you solve multi-step equations with fractions?
2. What happens if the equation has variables on both sides?
3. How do you check if your solution to an equation is correct?
4. How do you solve equations with decimals?
5. What is the difference between solving linear and quadratic equations?

### Tip:
When solving equations, always aim to first simplify both sides and move all terms with variables to one side for easier calculation.

Learn how to solve the linear equation 5x + 1 = 3x - 2 with a step-by-step guide. This problem demonstrates key algebraic concepts such as simplifying equations and solving for a variable. Perfect for students in Grades 6-8.

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