Let's solve each equation step-by-step:

Problem 6

$-6 + \frac{x}{4} = -5$

1. Add $6$ to both sides to isolate $\frac{x}{4}$: $\frac{x}{4} = 1$
2. Multiply both sides by $4$ to solve for $x$: $x = 4$

Answer for Problem 6: $x = 4$

Problem 7

$-9x + 1 = -80$

1. Subtract $1$ from both sides: $-9x = -81$
2. Divide both sides by $-9$ to solve for $x$: $x = 9$

Answer for Problem 7: $x = 9$

Problem 8

$8 - 2x = 14$

1. Subtract $8$ from both sides: $-2x = 6$
2. Divide both sides by $-2$ to solve for $x$: $x = -3$

Answer for Problem 8: $x = -3$

Problem 9

$\frac{x + 9}{3} = 8$

1. Multiply both sides by $3$ to clear the fraction: $x + 9 = 24$
2. Subtract $9$ from both sides to solve for $x$: $x = 15$

Answer for Problem 9: $x = 15$

Problem 10

$9x - 16 = -7$

1. Add $16$ to both sides: $9x = 9$
2. Divide both sides by $9$ to solve for $x$: $x = 1$

Answer for Problem 10: $x = 1$

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

Here are 5 related questions for further practice:

1. Solve: $\frac{x}{5} - 3 = 4$
2. Solve: $7x + 5 = 54$
3. Solve: $-4 + \frac{x}{2} = 6$
4. Solve: $12 - 5x = -3$
5. Solve: $\frac{x + 8}{4} = 3$

Tip: Remember to perform the same operation on both sides of the equation to maintain equality.