To solve the equation \( 3\left(\frac{2}{3}a - \frac{1}{3}\right) = 5a + 3 \) for \( a \), follow these steps:

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

### Step 2: Substitute this into the original equation.
The equation becomes:
\[
2a - 1 = 5a + 3
\]

### Step 3: Move all terms involving \( a \) to one side and constants to the other side.
- Subtract \( 2a \) from both sides:
  \[
  -1 = 5a - 2a + 3
  \]
  Simplifying gives:
  \[
  -1 = 3a + 3
  \]

- Subtract \( 3 \) from both sides to isolate the term with \( a \):
  \[
  -1 - 3 = 3a
  \]
  Simplifying gives:
  \[
  -4 = 3a
  \]

### Step 4: Solve for \( a \).
- Divide both sides by \( 3 \):
  \[
  a = \frac{-4}{3}
  \]

Thus, the solution is \( a = -\frac{4}{3} \).

Would you like further details or have any questions?

Here are some related questions to consider:
1. How do you handle equations with fractions and variables?
2. What does it mean to isolate the variable in an equation?
3. How do you solve equations with variables on both sides?
4. What are common mistakes to avoid when solving algebraic equations?
5. How can you verify that your solution to an equation is correct?

**Tip:** Always simplify fractions before proceeding with other steps in solving an equation; it makes the process easier and helps avoid mistakes.

Learn how to solve the equation 3(2/3a - 1/3) = 5a + 3 with a detailed step-by-step solution. This problem involves algebraic equations and the distributive property, suitable for students in Grades 7-9.

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