To solve the equation \(3(5m - 7) - 2(9m - 11) = 4(8m - 13) - 17\), we need to follow these steps:

1. Distribute the coefficients inside the parentheses.
2. Combine like terms.
3. Isolate the variable \(m\).

Let's solve the equation step-by-step:

1. **Distribute the coefficients:**
   \[
   3(5m - 7) - 2(9m - 11) = 4(8m - 13) - 17
   \]
   \[
   3 \cdot 5m - 3 \cdot 7 - 2 \cdot 9m + 2 \cdot 11 = 4 \cdot 8m - 4 \cdot 13 - 17
   \]
   \[
   15m - 21 - 18m + 22 = 32m - 52 - 17
   \]

2. **Combine like terms:**
   \[
   (15m - 18m) + (-21 + 22) = 32m - 69
   \]
   \[
   -3m + 1 = 32m - 69
   \]

3. **Isolate the variable \(m\):**
   \[
   1 + 69 = 32m + 3m
   \]
   \[
   70 = 35m
   \]
   \[
   m = \frac{70}{35}
   \]
   \[
   m = 2
   \]

Therefore, the solution to the equation is \(m = 2\).

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. How do you solve linear equations with fractions?
2. What are the steps to solve quadratic equations?
3. Can you explain how to solve systems of equations?
4. What is the method for solving inequalities?
5. How do you solve equations with absolute values?

**Tip:** Always double-check your work by plugging the solution back into the original equation to verify it satisfies the equation.

Learn how to solve the linear equation 3(5m - 7) - 2(9m - 11) = 4(8m - 13) - 17 step-by-step. This problem involves algebraic concepts such as the distributive property and combining like terms. Suitable for students in Grades 7-9.

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