Let's solve the equation \( 7(2a + 1) = 5(a - 4) \).

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

\[
7(2a + 1) = 5(a - 4)
\]

Expanding:

\[
14a + 7 = 5a - 20
\]

### Step 2: Move terms involving \( a \) to one side
Subtract \( 5a \) from both sides:

\[
14a - 5a + 7 = -20
\]

This simplifies to:

\[
9a + 7 = -20
\]

### Step 3: Move constants to the other side
Subtract 7 from both sides:

\[
9a = -20 - 7
\]

\[
9a = -27
\]

### Step 4: Solve for \( a \)
Divide both sides by 9:

\[
a = \frac{-27}{9}
\]

\[
a = -3
\]

### Solution:
The value of \( a \) is \( -3 \).

Would you like a detailed explanation of any of these steps or have any questions?

Here are some related questions:
1. How do you solve equations involving fractions?
2. What is the method to solve equations with variables on both sides?
3. How do you solve quadratic equations?
4. How can you check your solution to an equation?
5. How do you solve equations with distributive property?

**Tip:** Always check your solution by plugging it back into the original equation to ensure it's correct!

Learn how to solve the linear equation 7(2a + 1) = 5(a - 4) with a detailed step-by-step explanation. This problem covers key algebraic concepts, including the distributive property and balancing methods for linear equations. Suitable for students in Grades 7-8.

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