5/3 parentheses 2X -6 parentheses +18 equals 2/3 parentheses X +3 parentheses -4

We are given the equation:

\[
\frac{5}{3}(2X - 6) + 18 = \frac{2}{3}(X + 3) - 4
\]

### Step-by-Step Solution:

1. **Distribute the fractions**:
   - On the left-hand side: \(\frac{5}{3}(2X - 6)\)
     \[
     \frac{5}{3}(2X) - \frac{5}{3}(6) = \frac{10X}{3} - 10
     \]
   - On the right-hand side: \(\frac{2}{3}(X + 3)\)
     \[
     \frac{2}{3}(X) + \frac{2}{3}(3) = \frac{2X}{3} + 2
     \]

   So the equation becomes:
   \[
   \frac{10X}{3} - 10 + 18 = \frac{2X}{3} + 2 - 4
   \]

2. **Simplify both sides**:
   - Left-hand side:
     \[
     \frac{10X}{3} + 8
     \]
   - Right-hand side:
     \[
     \frac{2X}{3} - 2
     \]

   Now, the equation is:
   \[
   \frac{10X}{3} + 8 = \frac{2X}{3} - 2
   \]

3. **Eliminate the fractions** by multiplying the entire equation by 3:
   \[
   10X + 24 = 2X - 6
   \]

4. **Solve for \(X\)**:
   - Move the terms involving \(X\) to one side:
     \[
     10X - 2X = -6 - 24
     \]
     \[
     8X = -30
     \]
   - Divide by 8:
     \[
     X = \frac{-30}{8} = \frac{-15}{4}
     \]

### Final Answer:
\[
X = \frac{-15}{4}
\]

Would you like a detailed explanation of any step? 

Here are 5 related questions:
1. How do you handle equations with multiple fractions?
2. What are the common mistakes when distributing fractions?
3. How can you check if a solution to an equation is correct?
4. What are some tips for solving multi-step algebraic equations?
5. Can you explain why we multiply the entire equation by 3 in step 3?

**Tip**: Always double-check your distribution when working with fractions in algebra!

Learn how to solve a linear equation involving fractions: 5/3 (2X - 6) + 18 = 2/3 (X + 3) - 4. This step-by-step solution covers algebraic concepts such as distributing fractions and eliminating fractions by multiplying both sides. Suitable for students in Grades 8-10.

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