https://file.aiquickdraw.com/mathbot/file/1727404593545xjeuph4e.jpg

https://file.aiquickdraw.com/mathbot/file/1727404630907zm7temqq.jpg

It looks like you've uploaded images of math exercises. I'll extract and solve some of the visible problems from them. Here's what I can see clearly:

### Problems from the images:
1. **Problem 7:**  
   \( 6a - 4 = 3a + 5 \)
   
2. **Problem 8:**  
   \( 2(4b - 6) = 4(3b - 7) \)

3. **Problem 9:**  
   \( 8(2r - 3) - r = 3(3r + 2) \)

4. **Problem 10:**  
   \( 3x - 8(2x + 3) = -6(2x + 5) \)

I'll solve these equations for you one by one.

### Problem 7:  
\( 6a - 4 = 3a + 5 \)

**Solution:**
\[
6a - 3a = 5 + 4
\]
\[
3a = 9
\]
\[
a = 3
\]

### Problem 8:  
\( 2(4b - 6) = 4(3b - 7) \)

Expanding both sides:
\[
8b - 12 = 12b - 28
\]

Rearrange:
\[
8b - 12b = -28 + 12
\]
\[
-4b = -16
\]
\[
b = 4
\]

### Problem 9:  
\( 8(2r - 3) - r = 3(3r + 2) \)

Expanding both sides:
\[
16r - 24 - r = 9r + 6
\]

Simplify:
\[
15r - 24 = 9r + 6
\]

Rearrange:
\[
15r - 9r = 6 + 24
\]
\[
6r = 30
\]
\[
r = 5
\]

### Problem 10:  
\( 3x - 8(2x + 3) = -6(2x + 5) \)

Expanding both sides:
\[
3x - 16x - 24 = -12x - 30
\]

Simplify:
\[
-13x - 24 = -12x - 30
\]

Rearrange:
\[
-13x + 12x = -30 + 24
\]
\[
-x = -6
\]
\[
x = 6
\]

---

### Summary of solutions:
1. \( a = 3 \)
2. \( b = 4 \)
3. \( r = 5 \)
4. \( x = 6 \)

Would you like more details on these solutions or help with additional problems?

### Related questions:
1. How would you solve an equation with fractions, like \( \frac{1}{2}(x + 3) = \frac{3}{4}(2x - 1) \)?
2. What happens if an equation has no solution?
3. Can equations like these have infinitely many solutions?
4. How do you check your solutions by substitution?
5. What are common mistakes to avoid when solving multi-step equations?

**Tip:** Always double-check your work by substituting your solution back into the original equation.

Learn how to solve basic linear equations, including 6a - 4 = 3a + 5 and 3x - 8(2x + 3) = -6(2x + 5), with step-by-step solutions. This problem set covers key algebraic concepts and is suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation