Let's solve the equations one by one.

1) $2x + 10 = 14$

Step 1: Subtract 10 from both sides: $2x = 14 - 10$ $2x = 4$

Step 2: Divide both sides by 2: $x = \frac{4}{2} = 2$

Solution: $x = 2$

2) $\frac{x}{3} - 4 = 10$

Step 1: Add 4 to both sides: $\frac{x}{3} = 10 + 4$ $\frac{x}{3} = 14$

Step 2: Multiply both sides by 3: $x = 14 \times 3$ $x = 42$

Solution: $x = 42$

3) $5x + 25 = 10x$

Step 1: Subtract $5x$ from both sides: $25 = 10x - 5x$ $25 = 5x$

Step 2: Divide both sides by 5: $x = \frac{25}{5} = 5$

Solution: $x = 5$

4) $2(x + 4) = 4x + 18$

Step 1: Expand the left-hand side: $2x + 8 = 4x + 18$

Step 2: Subtract $2x$ from both sides: $8 = 2x + 18$

Step 3: Subtract 18 from both sides: $8 - 18 = 2x$ $-10 = 2x$

Step 4: Divide both sides by 2: $x = \frac{-10}{2} = -5$

Solution: $x = -5$

Do you want any additional details or explanations for any step?

Here are five related questions:

1. How would you solve equations involving fractions on both sides?
2. What are the steps to solve an equation with variables on both sides?
3. How do you check the solution to an equation?
4. How do you solve quadratic equations?
5. What happens when there is no solution to a linear equation?

Tip: Always perform the same operation on both sides of an equation to maintain balance.