We will solve the equation step by step:

\[
6 + 5(p - 1) = 46
\]

### Step 1: Expand the equation
Distribute the \(5\) across \((p - 1)\):

\[
6 + 5p - 5 = 46
\]

### Step 2: Combine like terms
Simplify \(6 - 5\) on the left side:

\[
1 + 5p = 46
\]

### Step 3: Isolate the variable
Subtract \(1\) from both sides:

\[
5p = 46 - 1
\]

\[
5p = 45
\]

### Step 4: Solve for \(p\)
Divide both sides by \(5\):

\[
p = \frac{45}{5}
\]

\[
p = 9
\]

Thus, the solution is \(p = 9\).

Do you need more details, or have any questions?

Here are five related questions:
1. What happens if the equation had a different constant on the right side?
2. How do you solve for \(p\) if there's a quadratic expression involved?
3. Can we solve this equation graphically?
4. What if the distributive property involved more terms, like \(5(p - 1 + x)\)?
5. How would you solve the equation if decimals were involved instead of integers?

**Tip:** Always distribute carefully and combine like terms before isolating the variable in algebraic equations.

Learn how to solve the linear equation 6 + 5(p - 1) = 46 using distributive property and algebraic methods. This detailed solution guides through expanding the equation, combining like terms, and isolating the variable. Suitable for students in Grades 6-8.

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