We need to solve the equation for \( g \):

\[
12g = 12\left(\dfrac{2}{3}g - 1\right) + 11
\]

### Step 1: Distribute the 12 on the right side
Distribute the \( 12 \) across \( \dfrac{2}{3}g \) and \( -1 \):

\[
12g = 12 \times \dfrac{2}{3}g - 12 \times 1 + 11
\]
\[
12g = 8g - 12 + 11
\]

### Step 2: Combine like terms on the right-hand side
\[
12g = 8g - 1
\]

### Step 3: Move all terms involving \( g \) to one side of the equation
Subtract \( 8g \) from both sides:
\[
12g - 8g = -1
\]
\[
4g = -1
\]

### Step 4: Solve for \( g \)
Divide both sides by 4:
\[
g = \dfrac{-1}{4}
\]
\[
g = -\dfrac{1}{4}
\]

### Final Answer:
The solution is \( g = -\dfrac{1}{4} \).

Do you want further details on any of these steps or have any questions? Here are five related questions you might find interesting:

1. How would the equation change if the constants on the right side were different?
2. How do you handle similar problems when dealing with fractions and variables?
3. What happens if you have variables on both sides with different coefficients?
4. How does solving for \( g \) change if instead of 12 you had a different coefficient?
5. How do you verify the solution once you've found it?

**Tip**: Always distribute carefully to avoid mistakes, especially when working with negative signs and fractions.

Learn how to solve the equation 12g = 12(2/3g - 1) + 11 step-by-step with a detailed solution. This problem involves algebraic equations with fractions and the distributive property. Suitable for students in Grades 7-9.

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