We need to solve the equation \( 2.5x + 3 = 3x - 2 \).

### Steps:
1. Subtract \( 2.5x \) from both sides to move all \( x \)-terms to the right:
   \[
   3 = 0.5x - 2
   \]

2. Add 2 to both sides to isolate the \( x \)-term:
   \[
   5 = 0.5x
   \]

3. Finally, divide both sides by 0.5:
   \[
   x = \frac{5}{0.5} = 10
   \]

So, the solution is \( x = 10 \).

Would you like any further details or have any questions?

Here are some related questions:
1. How do you solve equations with fractions or decimals?
2. What happens if both sides of the equation have multiple \( x \)-terms?
3. How do you check if your solution to an equation is correct?
4. What if the equation had no solution or infinite solutions?
5. How would the solution change if the equation included \( x^2 \)?

**Tip:** Always double-check your solution by substituting it back into the original equation to ensure both sides are equal.

Learn how to solve the linear equation 2.5x + 3 = 3x - 2 with a detailed step-by-step solution. This problem covers key algebraic concepts like solving equations with variables on both sides. Suitable for students in Grades 7-9.

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