To solve the equation \( \frac{2x - 3}{3} = \frac{x + 8}{2} \), we follow these steps:

### Step 1: Eliminate the denominators
To get rid of the fractions, multiply both sides by the least common denominator (LCD), which is 6 (the LCD of 3 and 2). So, multiply both sides of the equation by 6:

\[
6 \times \frac{2x - 3}{3} = 6 \times \frac{x + 8}{2}
\]

This simplifies to:

\[
2 \times (2x - 3) = 3 \times (x + 8)
\]

### Step 2: Distribute the numbers
Now, distribute the 2 and 3 on both sides:

\[
4x - 6 = 3x + 24
\]

### Step 3: Isolate the variable
Move all the terms with \( x \) to one side and constants to the other:

\[
4x - 3x = 24 + 6
\]

\[
x = 30
\]

### Final Answer:
The solution is \( x = 30 \).

Do you have any questions, or would you like more details on any of the steps?

Here are 5 questions that expand on the solution:
1. What happens if we had a different LCD?
2. How do we check if the solution is correct?
3. What are other methods to solve equations with fractions?
4. What if the equation had terms with higher powers of \( x \)?
5. How would this problem change if it had inequalities instead of an equation?

**Tip**: Always check your solution by substituting the value of \( x \) back into the original equation to verify your work.

Discover how to solve the linear equation with fractions, 2x - 3/3 = x + 8/2, using cross-multiplication and step-by-step instructions. This solution covers key algebraic concepts such as eliminating fractions and isolating variables, ideal for students in Grades 6-8.

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