((x+1) + (x+7))/(3) + (x)/(2) = 5

$$\frac{(x+1) + (x+7)}{3} + \frac{x}{2} = 5$$ $$\frac{2x+8}{3} + \frac{x}{2} = 5$$

Multiply the entire equation by 6.

$$6 \left( \frac{2x+8}{3} \right) + 6 \left( \frac{x}{2} \right) = 6 \times 5$$ $$2(2x+8) + 3x = 30$$

$$4x + 16 + 3x = 30$$ $$7x + 16 = 30$$

$$7x = 30 - 16$$ $$7x = 14$$ $$x = \frac{14}{7}$$ $$x = 2$$

The correct option is 2) 2.
The final answer is $\boxed{\text{2}}$.

2.
We need to solve the equation $\frac{x}{3} - \frac{7}{9} = \frac{20}{9}$.

$$\frac{x}{3} = \frac{20}{9} + \frac{7}{9}$$ $$\frac{x}{3} = \frac{20+7}{9}$$ $$\frac{x}{3} = \frac{27}{9}$$

$$x = 3 \times 3$$ $$x = 9$$

The correct option is 3) 9.
The final answer is $\boxed{\text{9}}$.

3.
We need to solve the equation $\frac{3x}{2} + 4 = 4x - 11$.

$$2 \left( \frac{3x}{2} + 4 \right) = 2(4x - 11)$$ $$3x + 8 = 8x - 22$$

$$8 + 22 = 8x - 3x$$ $$30 = 5x$$

$$x = \frac{30}{5}$$ $$x = 6$$

The correct option is 3) 6.
The final answer is $\boxed{\text{6}}$.

4.
We need to solve the equation $2x - 8 - 3x = x - 12$.

$$(2x - 3x) - 8 = x - 12$$ $$-x - 8 = x - 12$$

$$-8 + 12 = x + x$$ $$4 = 2x$$

$$x = \frac{4}{2}$$ $$x = 2$$

The correct option is 2) 2.
The final answer is $\boxed{\text{2}}$.

5.
We need to solve the equation $\frac{7y}{3} - 4 = \frac{2y}{6} + 8$.

$$3 \left( \frac{7y}{3} - 4 \right) = 3 \left( \frac{y}{3} + 8 \right)$$ $$7y - 12 = y + 24$$

$$7y - y = 24 + 12$$ $$6y = 36$$

$$y = \frac{36}{6}$$ $$y = 6$$

The final answer is $\boxed{\text{6}}$.