The image contains several linear equations that need to be solved for the variable. I’ll go through each problem one by one, providing the solutions and explanations.

1. Equation:

$-7 + 2n = 8 - 3n$

Solution:

1. Add $3n$ to both sides: $-7 + 5n = 8$
2. Add $7$ to both sides: $5n = 15$
3. Divide both sides by $5$: $n = 3$

2. Equation:

$-11 + 6x = 1 + 8x$

Solution:

1. Subtract $6x$ from both sides: $-11 = 1 + 2x$
2. Subtract $1$ from both sides: $-12 = 2x$
3. Divide both sides by $2$: $x = -6$

3. Equation:

$v - 8v = 2v$

Solution:

1. Combine like terms on the left side: $-7v = 2v$
2. Add $7v$ to both sides: $0 = 9v$
3. This equation results in: $v = 0$

4. Equation:

$-2 - 4n = 10 - 6n$

Solution:

1. Add $6n$ to both sides: $-2 + 2n = 10$
2. Add $2$ to both sides: $2n = 12$
3. Divide both sides by $2$: $n = 6$

5. Equation:

$1 - 4x = -15 - 2x$

Solution:

1. Add $4x$ to both sides: $1 = -15 + 2x$
2. Add $15$ to both sides: $16 = 2x$
3. Divide both sides by $2$: $x = 8$

6. Equation:

$4n + 3 = -7 + 2n$

Solution:

1. Subtract $2n$ from both sides: $2n + 3 = -7$
2. Subtract $3$ from both sides: $2n = -10$
3. Divide both sides by $2$: $n = -5$

7. Equation:

$2x + 8 = 1 - 5x$

Solution:

1. Add $5x$ to both sides: $7x + 8 = 1$
2. Subtract $8$ from both sides: $7x = -7$
3. Divide both sides by $7$: $x = -1$

8. Equation:

$11 + 5 + 3a - 7a = 8a - 8a$

Solution:

1. Simplify the left side by combining like terms: $16 - 4a = 0$
2. Add $4a$ to both sides: $16 = 4a$
3. Divide both sides by $4$: $a = 4$

Would you like any specific details on these solutions or have any additional questions?

Additional Practice Questions

1. Can you solve the equation $5y - 7 = 3y + 1$?
2. How do you handle an equation like $-2x + 5 = 3 - x$?
3. What would be the solution to the equation $8m + 2 = 2m + 14$?
4. How do you verify your solution to a linear equation?
5. What happens if you have a linear equation with no solution?

Tip: Always isolate the variable by performing inverse operations on both sides of the equation.