Let's solve these equations one by one.

28. $5s - 13 = s - 1$

Step 1: Move $s$ from the right side to the left side: $5s - s = -1 + 13$ Step 2: Simplify: $4s = 12$ Step 3: Solve for $s$: $s = \frac{12}{4} = 3$ Solution: $s = 3$

30. $2x + (2x - 3) = 5$

Step 1: Simplify the left side: $2x + 2x - 3 = 5$ Step 2: Combine like terms: $4x - 3 = 5$ Step 3: Move $-3$ to the other side: $4x = 5 + 3$ Step 4: Solve for $x$: $4x = 8 \quad \Rightarrow \quad x = \frac{8}{4} = 2$ Solution: $x = 2$

32. $4a + 17 = 7(a + 2)$

Step 1: Distribute the 7 on the right side: $4a + 17 = 7a + 14$ Step 2: Move $7a$ to the left side and $17$ to the right side: $4a - 7a = 14 - 17$ Step 3: Simplify: $-3a = -3$ Step 4: Solve for $a$: $a = \frac{-3}{-3} = 1$ Solution: $a = 1$

34. $5(r + 4) = -2(r - 3)$

Step 1: Distribute both sides: $5r + 20 = -2r + 6$ Step 2: Move $-2r$ to the left side and $20$ to the right side: $5r + 2r = 6 - 20$ Step 3: Simplify: $7r = -14$ Step 4: Solve for $r$: $r = \frac{-14}{7} = -2$ Solution: $r = -2$

Would you like more details on any specific step?

Related Questions:

1. What is the process for solving equations with variables on both sides?
2. How do you solve equations involving parentheses and distribution?
3. What happens when all terms cancel out in an equation?
4. Can you show how to check your solution in each equation?
5. What methods are used to simplify equations before solving?

Tip: Always check your solutions by plugging them back into the original equation to verify they satisfy the equation.