Let's solve the equation step by step:

Given equation:
\[
8(3g + 2) - 3g = 3(5g - 4) - 2
\]

### Step 1: Distribute the constants.
\[
8 \times (3g) + 8 \times (2) - 3g = 3 \times (5g) - 3 \times (4) - 2
\]
\[
24g + 16 - 3g = 15g - 12 - 2
\]

### Step 2: Combine like terms.
On the left side:
\[
24g - 3g + 16 = 21g + 16
\]

On the right side:
\[
15g - 12 - 2 = 15g - 14
\]

So now we have:
\[
21g + 16 = 15g - 14
\]

### Step 3: Move the \(g\) terms to one side and constants to the other.
Subtract \(15g\) from both sides:
\[
21g - 15g + 16 = -14
\]
\[
6g + 16 = -14
\]

Subtract 16 from both sides:
\[
6g = -14 - 16
\]
\[
6g = -30
\]

### Step 4: Solve for \(g\).
Divide by 6:
\[
g = \frac{-30}{6}
\]
\[
g = -5
\]

### Final Answer:
\[
g = -5
\]

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

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Here are 5 related questions to explore further:
1. How would the solution change if the constant term on the right side were different?
2. Can you verify the solution by substituting \( g = -5 \) back into the original equation?
3. What if the equation had a quadratic term, how would the solution approach differ?
4. How do you solve equations involving fractions?
5. What are some real-world applications of solving linear equations like this one?

**Tip:** When solving equations, always remember to check your solution by substituting it back into the original equation to ensure accuracy.

Learn how to solve the linear equation 8(3g + 2) - 3g = 3(5g - 4) - 2 with detailed step-by-step instructions. This problem covers key algebraic concepts such as linear equations, distributive property, combining like terms, and solving equations. Suitable for students in Grades 7-9.

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