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The problem presented is:

\[
\frac{1}{2}y - \frac{3}{5}x = -6
\]
You are asked to find the value of \(6x - 5y\).

### Step 1: Solve for one variable
We will first isolate one of the variables from the given equation. Let's solve for \(y\) in terms of \(x\).

Multiply the entire equation by 10 to eliminate the fractions:

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

This simplifies to:

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

### Step 2: Rearrange the equation
Now, solve for \(5y - 6x\):

\[
5y - 6x = 60
\]

Notice that this is exactly the negative of what we are looking for, as the problem asks for \(6x - 5y\

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

This problem involves solving for the expression 6x - 5y given the linear equation (1/2)y - (3/5)x = -6. It demonstrates core algebraic concepts such as equation manipulation and solving for variables. Suitable for students in Grades 9-10.

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