To solve the equation \( \frac{3}{2}x + 7 = \frac{5}{3}(x - 2) \), we can follow these steps:

1. **Distribute** the \( \frac{5}{3} \) on the right-hand side:
   \[
   \frac{3}{2}x + 7 = \frac{5}{3}x - \frac{10}{3}
   \]

2. **Eliminate the fractions** by finding the least common denominator (LCD), which is 6. Multiply the entire equation by 6:
   \[
   6 \times \left(\frac{3}{2}x + 7\right) = 6 \times \left(\frac{5}{3}x - \frac{10}{3}\right)
   \]
   This simplifies to:
   \[
   9x + 42 = 10x - 20
   \]

3. **Move the variables to one side** by subtracting \( 9x \) from both sides:
   \[
   42 = x - 20
   \]

4. **Isolate \( x \)** by adding 20 to both sides:
   \[
   x = 62
   \]

So, the solution is \( x = 62 \).

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. What happens if you change the constant on the left side from 7 to 10?
2. How would the solution change if the equation were \( \frac{3}{2}x + 7 = \frac{5}{4}(x - 2) \)?
3. How can you solve the equation using substitution or graphing methods?
4. What is the general approach to solving equations involving fractions?
5. How do you handle equations with variables on both sides in a real-world scenario?

**Tip:** Always simplify fractions and distribute terms first to make equations easier to solve.

Discover how to solve the linear equation 3/2x + 7 = 5/3(x - 2) step-by-step. This problem includes concepts like fraction elimination and isolating variables, making it perfect for students in Grades 8-10.

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