To complete the proof for the given equation $\frac{4(x - 3)}{3} = 4$, let's solve for $x$ step by step.

Step 1: Eliminate the denominator

Multiply both sides of the equation by 3 to remove the denominator on the left-hand side:

$\frac{4(x - 3)}{3} \times 3 = 4 \times 3$

This simplifies to:

$4(x - 3) = 12$

Step 2: Distribute the 4 on the left-hand side

Apply the distributive property to expand $4(x - 3)$:

$4x - 12 = 12$

Step 3: Isolate the variable term

Add 12 to both sides to move the constant term:

$4x - 12 + 12 = 12 + 12$

Simplifying this:

$4x = 24$

Step 4: Solve for $x$

Now, divide both sides by 4 to isolate $x$:

$x = \frac{24}{4}$

$x = 6$

Conclusion

The solution to the equation is $x = 6$.

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Would you like more details or have any questions about this process?

Here are 5 related questions for further exploration:

1. How do you solve similar equations with different coefficients?
2. What is the importance of the distributive property in algebra?
3. Can you solve for $x$ if the equation had decimals instead of fractions?
4. How does this proof change if the original equation includes negative coefficients?
5. What are the implications of having multiple terms inside the parentheses?

Tip: Always ensure you isolate the variable step by step, starting by eliminating fractions or parentheses first.