https://file.aiquickdraw.com/mathbot/file/1728106063417kxo87rn7.jpg

I see you've uploaded an image with several algebraic equations. Let's go through each one to solve them step by step.

### Top Row:
1. **Equation 1:**
   \[
   8z = 7z - 7
   \]
   Subtract \(7z\) from both sides:
   \[
   8z - 7z = -7 \implies z = -7
   \]

2. **Equation 2:**
   \[
   7z = 39 - 6z
   \]
   Add \(6z\) to both sides:
   \[
   7z + 6z = 39 \implies 13z = 39
   \]
   Now divide by 13:
   \[
   z = 39 / 13 = 3
   \]

3. **Equation 3:**
   \[
   5q = 44 - 6q
   \]
   Add \(6q\) to both sides:
   \[
   5q + 6q = 44 \implies 11q = 44
   \]
   Now divide by 11:
   \[
   q = 44 / 11 = 4
   \]

### Middle Row:
4. **Equation 4:**
   \[
   -12a - 8 = -16a
   \]
   Add \(12a\) to both sides:
   \[
   -8 = -16a + 12a \implies -8 = -4a
   \]
   Now divide by \(-4\):
   \[
   a = -8 / -4 = 2
   \]

5. **Equation 5:**
   \[
   9k = 8k - 11
   \]
   Subtract \(8k\) from both sides:
   \[
   9k - 8k = -11 \implies k = -11
   \]

6. **Equation 6:**
   \[
   b = -4b - 15
   \]
   Add \(4b\) to both sides:
   \[
   b + 4b = -15 \implies 5b = -15
   \]
   Now divide by 5:
   \[
   b = -15 / 5 = -3
   \]

### Bottom Row:
7. **Equation 7:**
   \[
   4x + 36 = 10x
   \]
   Subtract \(4x\) from both sides:
   \[
   36 = 6x
   \]
   Now divide by 6:
   \[
   x = 36 / 6 = 6
   \]

8. **Equation 8:**
   \[
   c = -3c - 20
   \]
   Add \(3c\) to both sides:
   \[
   c + 3c = -20 \implies 4c = -20
   \]
   Now divide by 4:
   \[
   c = -20 / 4 = -5
   \]

9. **Equation 9:**
   \[
   6x + 27 = 9x
   \]
   Subtract \(6x\) from both sides:
   \[
   27 = 3x
   \]
   Now divide by 3:
   \[
   x = 27 / 3 = 9
   \]

---

Would you like any more detailed steps for a specific equation? Here are some related questions to consider:

1. What happens if both variables have the same coefficient?
2. How do you deal with negative variables?
3. What do you do when a variable appears on both sides of the equation?
4. How can you check if your solution is correct?
5. How do equations change when fractions are involved?

**Tip:** Always simplify the equation as much as possible before solving it to avoid unnecessary steps.

Solve the following algebraic equations:
1. 8z = 7z - 7
2. 7z = 39 - 6z
3. 5q = 44 - 6q
4. -12a - 8 = -16a
5. 9k = 8k - 11
6. b = -4b - 15
7. 4x + 36 = 10x
8. c = -3c - 20
9. 6x + 27 = 9x

Learn how to solve a set of algebraic equations where variables appear on both sides. This exercise covers the key concepts of isolating variables and using properties of equality. Detailed steps are provided for each equation, suitable for Grades 6-8.

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