Let's go through each equation from the image and solve it step-by-step to match it with the correct solution.

1. Equation: $4 + x = -8x - 5$

   • Combine like terms: $x + 8x = -5 - 4$ $9x = -9$ $x = -1$
   • Solution: $x = -1$

2. Equation: $2(5x + 2) = 10x - 4$

   • Expand both sides: $10x + 4 = 10x - 4$
   • Subtract $10x$ from both sides: $4 = -4$
   • This is a contradiction, so there is no solution.

3. Equation: $7 + 2x = 2x - 7$

   • Subtract $2x$ from both sides: $7 = -7$
   • This is also a contradiction, so there is no solution.

4. Equation: $-3x + 3 = 3(1 - x)$

   • Expand the right-hand side: $-3x + 3 = 3 - 3x$
   • Add $3x$ to both sides: $3 = 3$
   • This is always true, meaning the solution is $x =$ all real numbers.

Final Matching:

1. $4 + x = -8x - 5$ → $x = -1$
2. $2(5x + 2) = 10x - 4$ → No solution
3. $7 + 2x = 2x - 7$ → No solution
4. $-3x + 3 = 3(1 - x)$ → $x =$ all real numbers

Would you like further explanations or more details on any of the steps?

Here are 5 related questions:

1. How do you determine when an equation has no solution?
2. Can an equation have more than one solution?
3. What does it mean for an equation to have "all real numbers" as a solution?
4. How would you solve more complex multi-variable equations?
5. What are the different types of contradictions in equations?

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