Let's solve the equation step by step:

### Given equation:

\[
\frac{G}{3} + 6 = 5 \left( (7 - 4)(3 - 8) \right)
\]

### Step 1: Simplify the expression inside the parentheses.

First, simplify \((7 - 4)\) and \((3 - 8)\):

\[
(7 - 4) = 3 \quad \text{and} \quad (3 - 8) = -5
\]

So, we have:

\[
5 \left( 3 \times (-5) \right) = 5 \times (-15) = -75
\]

Now, substitute this back into the equation:

\[
\frac{G}{3} + 6 = -75
\]

### Step 2: Isolate \(\frac{G}{3}\).

Subtract 6 from both sides:

\[
\frac{G}{3} = -75 - 6 = -81
\]

### Step 3: Solve for \(G\).

Multiply both sides by 3:

\[
G = -81 \times 3 = -243
\]

### Final Answer:
\[
G = -243
\]

Would you like more details or further clarifications on this?

Here are 5 related questions to explore this further:
1. What happens if the sign in front of the \(-5\) were different?
2. How do you handle solving fractions with variables?
3. What if the constant on the right-hand side were positive?
4. Can you derive a similar equation with more terms?
5. How do you verify if your solution is correct?

**Tip:** Always simplify expressions inside parentheses first to avoid mistakes in larger equations.

Learn how to solve the algebraic equation G/3 + 6 = 5(7-4)(3-8) with a detailed step-by-step explanation. This problem covers essential algebra concepts, including the simplification of expressions and applying the order of operations. Suitable for students in Grades 8-10.

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