The given equation is:

\[
2m = -6n - 5
\]

We can solve this equation for either \( m \) or \( n \). Let's solve for \( m \) first.

### Step 1: Solve for \( m \)

To isolate \( m \), divide both sides of the equation by 2:

\[
m = \frac{-6n - 5}{2}
\]

Thus, the equation solved for \( m \) is:

\[
m = -3n - \frac{5}{2}
\]

### Step 2: Solve for \( n \) (if desired)

If you'd like to solve for \( n \) instead, rearrange the original equation:

\[
2m = -6n - 5
\]

Add 6n to both sides:

\[
2m + 6n = -5
\]

Now, solve for \( n \) by subtracting \( 2m \) and dividing by 6:

\[
n = \frac{-5 - 2m}{6}
\]

Thus, the equation solved for \( n \) is:

\[
n = \frac{-5}{6} - \frac{m}{3}
\]

Do you want further details or clarifications?

### 5 Related Questions:
1. How would the solution change if there was an additional constant on the right side?
2. Can you graph the relationship between \( m \) and \( n \)?
3. What is the slope of the line if we treat \( m \) as a function of \( n \)?
4. How can we rewrite the equation in standard form?
5. What happens to the solution if we substitute specific values for \( n \)?

### Tip:
Always simplify the equation as much as possible to make it easier to manipulate and interpret.

Explore how to solve the linear equation 2m = -6n - 5 with a clear, step-by-step guide. This problem covers essential algebraic concepts, including solving for variables in linear equations. Suitable for students in Grades 7-9.

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