Let's solve the equation step by step:

\[
4(4m - 3) - 1(m - 5) = -52
\]

### Step 1: Distribute the constants inside the parentheses.

\[
4 \times (4m) + 4 \times (-3) - 1 \times (m) + 1 \times 5 = -52
\]

This simplifies to:

\[
16m - 12 - m + 5 = -52
\]

### Step 2: Combine like terms.

\[
(16m - m) + (-12 + 5) = -52
\]

\[
15m - 7 = -52
\]

### Step 3: Add 7 to both sides of the equation.

\[
15m - 7 + 7 = -52 + 7
\]

\[
15m = -45
\]

### Step 4: Divide both sides by 15 to solve for \( m \).

\[
m = \frac{-45}{15}
\]

\[
m = -3
\]

Thus, the solution is:

\[
m = -3
\]

Do you want further details on any step or have any other questions?

Here are 5 related questions to expand on this:
1. How do you solve equations involving variables on both sides?
2. How do you handle equations with multiple parentheses?
3. What are like terms, and why is combining them important?
4. How can you verify that your solution to an equation is correct?
5. What are some strategies for solving more complex linear equations?

**Tip:** Always distribute carefully and combine like terms to simplify the equation before solving!

Learn how to solve the linear equation 4(4m - 3) - 1(m - 5) = -52 using distributive property and combining like terms. This problem walks through step-by-step simplification and solution suitable for students in Grades 8-10.

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