Let's solve the equation \( 3x + 9 = 2.5x + 14 \).

1. Start by subtracting \( 2.5x \) from both sides to get all the terms involving \( x \) on one side:
   \[
   3x - 2.5x + 9 = 14
   \]
   This simplifies to:
   \[
   0.5x + 9 = 14
   \]

2. Now subtract 9 from both sides:
   \[
   0.5x = 14 - 9
   \]
   \[
   0.5x = 5
   \]

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

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

Would you like more details or have any questions?

Here are some related questions to explore:
1. What happens if we substitute \( x = 10 \) back into the original equation?
2. How do you solve an equation with fractions?
3. Can you explain how to solve equations with variables on both sides?
4. What if the equation had decimals in more places, like \( 3.25x \)?
5. How do you check if an equation has no solution?

**Tip:** When solving equations, it's helpful to first isolate the variable terms on one side for easier calculation.

Learn how to solve the linear equation 3x + 9 = 2.5x + 14 step-by-step. This tutorial covers essential algebraic concepts, such as manipulating equations with variables on both sides. Perfect for students in Grades 6-8 looking to master basic algebra.

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