To solve the equation \(3(1 - 3p) = 6(p - 7)\), let's start by expanding both sides and then isolating the variable \(p\).

### Step 1: Expand both sides of the equation

\[
3(1 - 3p) = 6(p - 7)
\]

Expand the left side:

\[
3 \cdot 1 - 3 \cdot 3p = 3 - 9p
\]

Expand the right side:

\[
6 \cdot p - 6 \cdot 7 = 6p - 42
\]

So, the equation becomes:

\[
3 - 9p = 6p - 42
\]

### Step 2: Combine like terms

Move all terms involving \(p\) to one side and constant terms to the other side. To do this, add \(9p\) to both sides and add \(42\) to both sides:

\[
3 + 42 = 6p + 9p
\]

Simplify:

\[
45 = 15p
\]

### Step 3: Solve for \(p\)

Divide both sides by 15 to isolate \(p\):

\[
p = \frac{45}{15}
\]

\[
p = 3
\]

### Solution

The solution to the equation is:

\[
\boxed{p = 3}
\]

Would you like to see more details, or do you have any other questions?

### Related Questions

1. What is the general process for solving linear equations involving a single variable?
2. How do you solve equations with variables on both sides?
3. How can you check if your solution to an equation is correct?
4. What are some common mistakes to avoid when solving linear equations?
5. How do linear equations relate to real-world problems?

**Tip:** Always double-check your solution by substituting it back into the original equation to verify it works.

Learn how to solve the linear equation 3(1-3p) = 6(p-7) with step-by-step guidance. This problem covers key algebraic concepts such as the distributive property and solving linear equations with variables on both sides. Suitable for students in Grades 6-8.

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