Let's evaluate each solution in the image:

Problem 21:

The equation is given as: $-2(7 - y) + 4 = -4$

The steps shown are:

1. $-2(7 - y) + 4 = -4$
2. $-14 + 2y + 4 = -4$
3. $-10 + 2y = -4$
4. $2y = 6$
5. $y = 3$

Correction: The final step shows $y = -3$, but after solving correctly: $y = 3$

So the friend made an error in the last step. The correct solution is $y = 3$.

Problem 22:

The equation is: $3(y - 1) + 8 = 11$

The steps shown are:

1. $3(y - 1) + 8 = 11$
2. $3y - 3 + 8 = 11$
3. $3y + 5 = 11$
4. $3y = 6$
5. $y = 2$

The solution is correct.

Conclusion:

• For problem 21, the friend is incorrect; the correct solution is $y = 3$, not $y = -3$.
• For problem 22, the friend is correct; $y = 2$.

Would you like further explanation on any of the steps?

Here are five related questions to deepen understanding:

1. How do you distribute the negative sign in problem 21?
2. What would happen if you missed distributing correctly in problem 22?
3. What is the significance of isolating the variable?
4. Can you solve an equation where the variable appears on both sides?
5. How do you check if your solution is correct by plugging it back into the original equation?

Tip: Always recheck the final step after solving equations to ensure no sign errors occur.