https://file.aiquickdraw.com/mathbot/file/1729200516446ctbtfwfv.jpg

The equation provided in the image is:

\[
4(p + 2) = 7p - 1
\]

Let's solve this step by step:

### Step 1: Expand the left-hand side
Distribute the 4 on the left-hand side:

\[
4p + 8 = 7p - 1
\]

### Step 2: Move all terms involving \( p \) to one side
To isolate \( p \), subtract \( 4p \) from both sides:

\[
8 = 7p - 4p - 1
\]
\[
8 = 3p - 1
\]

### Step 3: Move the constant terms to the other side
Add 1 to both sides:

\[
8 + 1 = 3p
\]
\[
9 = 3p
\]

### Step 4: Solve for \( p \)
Divide both sides by 3:

\[
p = \frac{9}{3} = 3
\]

### Step 5: Check the solution
Substitute \( p = 3 \) back into the original equation:

Original equation:
\[
4(p + 2) = 7p - 1
\]

Substitute \( p = 3 \):

\[
4(3 + 2) = 7(3) - 1
\]
\[
4(5) = 21 - 1
\]
\[
20 = 20
\]

Since both sides of the equation are equal, \( p = 3 \) is the correct solution.

---

Would you like more details on any part of the solution or have any further questions?

Here are some related questions you might want to explore:
1. How do you solve equations with variables on both sides?
2. What happens if an equation has no solution?
3. How do you solve equations with fractions?
4. How can you check if a solution to an equation is correct?
5. What are the steps to solve inequalities?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Solve 4(p + 2) = 7p - 1 and check the solution.

Learn how to solve and check the linear equation 4(p + 2) = 7p - 1 with a detailed step-by-step solution. This problem focuses on key algebraic concepts like distributing, combining like terms, and isolating variables. Ideal for students in Grades 8-10.

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