https://file.aiquickdraw.com/mathbot/file/17262566413151zuettmk.jpg

The equation given in the image is:

\[
\frac{1}{2}y - \frac{3}{5}x = -6
\]

You are asked to find the value of \( 6x - 5y \).

### Step-by-step Solution:

1. **Rewrite the equation:**

   \[
   \frac{1}{2}y - \frac{3}{5}x = -6
   \]

   To get rid of the fractions, multiply the whole equation by 10 (the least common denominator of 2 and 5):

   \[
   10 \left( \frac{1}{2}y \right) - 10 \left( \frac{3}{5}x \right) = 10(-6)
   \]

   This simplifies to:

   \[
   5y - 6x = -60
   \]

2. **Rearrange the equation:**

   \[
   -6x + 5y = -60
   \]

3. **Find \( 6x - 5y \):**

   Notice that \( 6x - 5y \) is just the negative of \( -6x + 5y \). So:

   \[
   6x - 5y = -( -6x + 5y )
   \]

   Therefore:

   \[
   6x - 5y = 60
   \]

### Final Answer:
The value of \( 6x - 5y \) is **60**.

---

Would you like more details or clarifications on any part? 

Here are 5 related questions to expand on this:

1. How do you solve linear equations involving fractions?
2. Can you always clear fractions by multiplying both sides of the equation?
3. What are some strategies to simplify algebraic expressions?
4. How can you verify the result of a linear equation?
5. How does the structure of an equation change when you multiply by negative values?

**Tip:** Multiplying an equation by the least common denominator is a great way to eliminate fractions and simplify your calculations!

If (1/2)y - (3/5)x = -6, what is the value of 6x - 5y?

Learn how to solve a linear equation involving fractions. The problem (1/2)y - (3/5)x = -6 asks for the value of 6x - 5y. Discover the steps to eliminate fractions and simplify the equation to get the correct answer.

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