Let's solve each equation step by step.

1. Equation: $2x = 10$
   To solve for $x$: $x = \frac{10}{2} = 5$ Solution: $x = 5$

2. Equation: $-3x = 21$
   To solve for $x$: $x = \frac{21}{-3} = -7$ Solution: $x = -7$

3. Equation: $\frac{1}{3}x = 6$
   To solve for $x$: $x = 6 \cdot 3 = 18$ Solution: $x = 18$

4. Equation: $-\frac{1}{2}x = -7$
   To solve for $x$: $x = \frac{-7}{-\frac{1}{2}} = -7 \cdot -2 = 14$ Solution: $x = 14$

Final Answers:

1. $x = 5$
2. $x = -7$
3. $x = 18$
4. $x = 14$

Would you like additional details or explanations?

Here are 5 related questions for you to consider:

1. How do you solve equations involving fractions?
2. What happens if there are variables on both sides of an equation?
3. How can you check the solution of an equation?
4. What are some examples of real-life applications of these equations?
5. How do equations change when additional terms are added to both sides?

Tip: Always double-check your solutions by substituting them back into the original equation!