To solve the equation \( 6\left(\frac{2}{3}a - 4\right) - 8\left(3 + \frac{1}{2}a\right) = -a \) for \( a \), follow these steps:

### Step 1: Distribute the constants inside the parentheses.
- Distribute \( 6 \) to \( \frac{2}{3}a \) and \( -4 \):
  \[
  6 \times \frac{2}{3}a = 4a, \quad 6 \times (-4) = -24
  \]
  So, \( 6\left(\frac{2}{3}a - 4\right) = 4a - 24 \).

- Distribute \( -8 \) to \( 3 \) and \( \frac{1}{2}a \):
  \[
  -8 \times 3 = -24, \quad -8 \times \frac{1}{2}a = -4a
  \]
  So, \( -8\left(3 + \frac{1}{2}a\right) = -24 - 4a \).

### Step 2: Substitute these into the original equation.
\[
4a - 24 - 24 - 4a = -a
\]

### Step 3: Combine like terms.
- Combine the constants on the left side:
  \[
  4a - 4a - 24 - 24 = -a
  \]
  This simplifies to:
  \[
  -48 = -a
  \]

### Step 4: Solve for \( a \).
- Multiply both sides by \(-1\) to isolate \( a \):
  \[
  a = 48
  \]

Thus, the solution is \( a = 48 \).

Would you like further details or have any questions?

Here are some related questions to consider:
1. How do you solve equations involving fractions and variables?
2. What is the distributive property and how is it used in solving equations?
3. Can equations with variables on both sides have no solution? How do you determine this?
4. How do you check if a solution to an equation is correct?
5. What are the steps to simplify algebraic expressions?

**Tip:** Always double-check your solution by substituting the value back into the original equation.

Learn how to solve the equation 6(2/3a - 4) - 8(3 + 1/2a) = -a using algebraic methods. This problem involves equations with fractions and variables, utilizing the distributive property to simplify terms. Suitable for students in Grades 7-9.

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