Let's solve each of these equations step by step.

a) $x + 5 = 2$: $x = 2 - 5 = -3$ Solution: $x = -3$.

b) $x + 54 = -33$: $x = -33 - 54 = -87$ Solution: $x = -87$.

c) $-74 + x = 14$: $x = 14 + 74 = 88$ Solution: $x = 88$.

d) $58 + x = 96$: $x = 96 - 58 = 38$ Solution: $x = 38$.

e) $27 = x + 46$: $x = 27 - 46 = -19$ Solution: $x = -19$.

f) $-43 = 19 + x$: $x = -43 - 19 = -62$ Solution: $x = -62$.

Would you like any additional details or have any questions?

Here are five related questions to explore further:

1. What would the solutions be if we changed the constants on the right-hand side of the equations?
2. How do these types of equations relate to linear functions on a graph?
3. What is the process for solving equations with variables on both sides?
4. How can we verify the solutions to each equation?
5. What is the impact of changing the signs in these equations on the solutions?

Tip: Always check your solution by substituting it back into the original equation to ensure both sides are equal.