https://file.aiquickdraw.com/mathbot/file/17301406219668y3xuxbp.jpg

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.

Learn how to solve a series of linear equations, including problems with fractions and negative coefficients. This guide covers step-by-step solutions for problems 6 to 10, helping students understand core algebraic concepts like isolating variables and maintaining equality.

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