Let's solve the equation step by step:

### Given equation:
\[
19 - 5(2m - 3) + 9m = 36
\]

### Step 1: Distribute the \(-5\) over the terms inside the parentheses:
\[
19 - 10m + 15 + 9m = 36
\]

### Step 2: Combine like terms on the left side:
\[
(19 + 15) + (-10m + 9m) = 36
\]
\[
34 - m = 36
\]

### Step 3: Subtract 34 from both sides to isolate \(m\):
\[
-m = 36 - 34
\]
\[
-m = 2
\]

### Step 4: Multiply both sides by \(-1\) to solve for \(m\):
\[
m = -2
\]

### Final solution:
\[
m = -2
\]

Would you like further details on any step, or do you have any questions?

### Related questions:
1. How do you solve equations with variables on both sides?
2. What are some examples of equations with distribution?
3. How does the distributive property work in algebra?
4. Can you show examples of solving equations involving parentheses?
5. How do you handle negative signs when solving equations?

### Tip: Always distribute multiplication before combining like terms when parentheses are involved.

Step-by-step solution to the linear equation 19 - 5(2m - 3) + 9m = 36. Learn how to apply the distributive property and combine like terms to isolate the variable m. Suitable for students in Grades 8-10.

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