Let's go through the set of equations one by one and solve them:

1. $x + 5 = 7$

To solve for $x$: $x = 7 - 5 = 2$

2. $2 + x = 7$

To solve for $x$: $x = 7 - 2 = 5$

3. $x + 8 = 6$

To solve for $x$: $x = 6 - 8 = -2$

4. $x - 3 = 12$

To solve for $x$: $x = 12 + 3 = 15$

5. $x + 15 = 20$

To solve for $x$: $x = 20 - 15 = 5$

6. $\frac{x}{3} = 4$

To solve for $x$: $x = 4 \times 3 = 12$

7. $3x - 12 = 0$

To solve for $x$: $3x = 12 \quad \Rightarrow \quad x = \frac{12}{3} = 4$

8. $2x - 3 = 5 + x$

To solve for $x$: $2x - x = 5 + 3 \quad \Rightarrow \quad x = 8$

9. $8x - 3 = 4 + 7x$

To solve for $x$: $8x - 7x = 4 + 3 \quad \Rightarrow \quad x = 7$

10. $\frac{x + 3}{3} + \frac{x}{3} - x = 2$

Combine the terms on the left: $\frac{(x + 3) + x}{3} - x = 2 \quad \Rightarrow \quad \frac{2x + 3}{3} - x = 2$ Multiply everything by 3 to eliminate the denominator: $2x + 3 - 3x = 6 \quad \Rightarrow \quad -x + 3 = 6 \quad \Rightarrow \quad -x = 6 - 3 = 3$ So: $x = -3$

All equations are now solved. Do you want any further details or explanations on a specific step?

Here are 5 related questions to test your understanding:

1. How would you solve an equation with fractions on both sides?
2. How do you check if a solution to an equation is correct?
3. Can an equation have more than one solution?
4. What are the steps to solve a quadratic equation?
5. How do you solve equations with variables on both sides?

Tip: Always check your solution by substituting it back into the original equation to verify it works.