To solve the equation

$-4a = 4 + \frac{2a + 7}{-3}$

we'll start by simplifying the right side and eliminating the fraction.

Step-by-Step Solution

1. Simplify the Fraction:

   The equation is:

   $-4a = 4 + \frac{2a + 7}{-3}$

   Rewrite the fraction:

   $-4a = 4 - \frac{2a + 7}{3}$

2. Eliminate the Fraction:

   Multiply every term by 3 to clear the fraction:

   $3(-4a) = 3 \left(4 - \frac{2a + 7}{3}\right)$

   This simplifies to:

   $-12a = 12 - (2a + 7)$

   Distribute the negative sign on the right:

   $-12a = 12 - 2a - 7$

   Combine like terms:

   $-12a = 5 - 2a$

3. Solve for $a$:

   Add $2a$ to both sides:

   $-12a + 2a = 5$

   Simplify:

   $-10a = 5$

   Divide both sides by $-10$:

   $a = -\frac{1}{2}$

Final Answer

$a = -\frac{1}{2}$

Would you like more details on any step, or do you have any questions?

Additional Related Questions:

1. How do you solve equations with multiple fractions?
2. What are the rules for multiplying and dividing both sides of an equation?
3. How can you check your solution in an algebraic equation?
4. What techniques are useful for isolating variables in equations?
5. How do you deal with equations involving negative numbers?

Tip: Always double-check your work by substituting the solution back into the original equation to verify it satisfies all terms.