Solve for g: 4 - (1/12)g - 2 = (3/2)g + 1 - (5/6)g.

Steps to Solve

1. Simplify both sides of the equation

Start with the original equation:
$$ 4 - \frac{1}{12}g - 2 = \frac{3}{2}g + 1 - \frac{5}{6}g $$

On the left side, simplify:
$$ 4 - 2 = 2 $$
So it becomes:
$$ 2 - \frac{1}{12}g = \frac{3}{2}g + 1 - \frac{5}{6}g $$

Next, simplify the right side by combining like terms:
Combine $\frac{3}{2}g$ and $-\frac{5}{6}g$.
Convert $\frac{3}{2}g$ to sixths:
$$ \frac{3}{2}g = \frac{9}{6}g $$
Thus, we have:
$$ \frac{9}{6}g - \frac{5}{6}g = \frac{4}{6}g = \frac{2}{3}g $$
So we update the equation to:
$$ 2 - \frac{1}{12}g = \frac{2}{3}g + 1 $$

2. Isolate g on one side

Focus on isolating $g$. Start by moving the terms with $g$ to one side and constant terms to the other side.
Subtract $1$ from both sides:
$$ 2 - 1 - \frac{1}{12}g = \frac{2}{3}g $$
This simplifies to:
$$ 1 - \frac{1}{12}g = \frac{2}{3}g $$

Now, add $\frac{1}{12}g$ to both sides:
$$ 1 = \frac{2}{3}g + \frac{1}{12}g $$

3. Combine g terms on the right side

To combine the $g$ terms, we need a common denominator. The least common multiple of $3$ and $12$ is $12$.

Convert $\frac{2}{3}g$ to twelfths:
$$ \frac{2}{3}g = \frac{8}{12}g $$

Now we have:
$$ 1 = \frac{8}{12}g + \frac{1}{12}g $$
This simplifies to:
$$ 1 = \frac{9}{12}g $$

4. Solve for g

To isolate $g$, multiply both sides by the reciprocal of $\frac{9}{12}$, which is $\frac{12}{9}$:
$$ g = 1 \times \frac{12}{9} $$
$$ g = \frac{12}{9} $$

Now simplify this fraction:
$$ g = \frac{4}{3} $$