https://file.aiquickdraw.com/mathbot/file/1729273984223jg4x4sc7.jpg

Let's solve the given equation:

\[
p - 2(4 - 3p) = 2p + 7
\]

### Step 1: Expand the parentheses on the left side
\[
p - 2 \cdot 4 + 2 \cdot 3p = 2p + 7
\]
\[
p - 8 + 6p = 2p + 7
\]

### Step 2: Combine like terms on each side
On the left side:
\[
p + 6p = 7p \quad \Rightarrow \quad 7p - 8 = 2p + 7
\]

### Step 3: Move all terms involving \(p\) to one side
\[
7p - 2p = 7 + 8
\]
\[
5p = 15
\]

### Step 4: Solve for \(p\)
\[
p = \frac{15}{5} = 3
\]

### Conclusion
Since we found a unique value for \(p\), the equation has **1 solution**. Therefore, the correct answer is:

\[
\boxed{1 \text{ solution}}
\]

---

Would you like a more detailed breakdown or have further questions?

### 5 Related Questions:
1. How do you determine if an equation has infinitely many solutions?
2. What changes in an equation would result in no solutions?
3. How can you verify that your solution to a linear equation is correct?
4. How do you solve equations with variables on both sides?
5. What happens when you solve a system of equations that have no solutions?

### Tip:
When solving equations with parentheses, always distribute first before combining terms to avoid mistakes.

How many solutions does the equation have? p - 2(4 - 3p) = 2p + 7

Learn how to solve the linear equation p - 2(4 - 3p) = 2p + 7 step by step. This problem involves basic algebra concepts and solving linear equations. Suitable for students in Grades 8-10.

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