https://file.aiquickdraw.com/mathbot/file/17267610951324zy8ucsq.jpg

The equation extracted from the image is:

\[
1 - 6 \cdot (3p + 4) = -10(p + 8)
\]

I will now solve this equation for \( p \).

Let's proceed with the solution:

### Step 1: Expand both sides
\[
1 - 6(3p + 4) = -10(p + 8)
\]
Expanding the terms:
\[
1 - (18p + 24) = -10p - 80
\]

### Step 2: Simplify the equation
\[
1 - 18p - 24 = -10p - 80
\]
\[
-18p - 23 = -10p - 80
\]

### Step 3: Move all terms involving \( p \) to one side and constants to the other side
\[
-18p + 10p = -80 + 23
\]
\[
-8p = -57
\]

### Step 4: Solve for \( p \)
\[
p = \frac{-57}{-8} = \frac{57}{8}
\]

Thus, the solution is \( p = \frac{57}{8} \).

Let me know if you'd like further details or have any questions.

Here are 5 related questions:
1. How can you verify if a solution satisfies a given equation?
2. What other techniques can be used to solve linear equations?
3. How do you interpret the result when dealing with fractional solutions?
4. What are common mistakes to avoid in simplifying and solving equations?
5. How can this method be applied to more complex algebraic expressions?

**Tip:** Always recheck your expanded terms to ensure you haven’t missed a sign or coefficient!

Solve the equation: 1 - 6(3p + 4) = -10(p + 8) for p.

Discover how to solve the linear equation 1 - 6(3p + 4) = -10(p + 8) with a clear, step-by-step solution. This problem explores key algebraic concepts such as the distributive property and basic linear equation solving, making it ideal for students in Grades 9-10.

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