https://file.aiquickdraw.com/mathbot/file/1727227074593n69n25wz.pdf

The document you've uploaded contains a set of one-step equations, followed by some word problems and expressions for simplification. Below, I'll solve the equations in sequence for clarity:

### One-Step Equations:
1. **x + 12 = 7**
   - Solution: $ x = 7 - 12 = -5 $

2. **4 = -0.8n**
   - Solution: $ n = \frac{4}{-0.8} = -5 $

3. **6 = -w/8**
   - Solution: $ w = 6 \times (-8) = -48 $

4. **5/6 = 1/3 + d**
   - Solution: $ d = \frac{5}{6} - \frac{1}{3} = \frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2} $

5. **x - 8π = π**
   - Solution: $ x = π + 8π = 9π $

6. **-4/5 = -5/6k**
   - Solution: $ k = \frac{-4/5}{-5/6} = \frac{24}{25} $

7. **7x = 35**
   - Solution: $ x = 35 / 7 = 5 $

8. **-2 = 6/7n**
   - Solution: $ n = \frac{-2 \times 7}{6} = -\frac{14}{6} = -\frac{7}{3} $

9. **72 = -m**
   - Solution: $ m = -72 $

10. **r/π = 7.3**
    - Solution: $ r = 7.3π $

11. **d - 2.8 ÷ 0.2 = -14**
    - Solution: $ d - 14 = -14 \implies d = -14 + 14 = 0 $

12. **m - (1/4) · 3 = -5/6**
    - Solution: $ m - 3/4 = -5/6 \implies m = -5/6 + 3/4 = \frac{-10 + 9}{12} = -1/12 $

### Word Problems:
13. **Concert Ticket Problem:**
    - Equation: $ p - 14.50 = 53 $
    - Solution: $ p = 53 + 14.50 = 67.50 $ (Original price of the ticket is $67.50)

14. **Account Balance Problem:**
    - Equation: $ 420 = \frac{7}{6} \times \text{Original balance} $
    - Solution: $ \text{Original balance} = \frac{420 \times 6}{7} = 360 $
    - Interest earned: $ 420 - 360 = 60 $

### Simplify the Expressions:
15. **4x + 9 - 6x - y**
    - Simplified: $ -2x + 9 - y $

16. **10 - 5(9n - 9)**
    - Simplified: $ 10 - 45n + 45 = 55 - 45n $

17. **-5n + 3(6 + 7n)**
    - Simplified: $ -5n + 18 + 21n = 16n + 18 $

### Extra Credit:
18. **12πx = 12π**
    - Solution: $ x = 1 $

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Would you like further details on any particular question? Here are 5 related problems you might find interesting:

1. Solve: $ 3x + 5 = 17 $
2. Simplify: $ 7(2x + 3) - 4x $
3. What is the original balance if 4/5 of it equals 320?
4. A discounted price is $25 less than the original price of $75. What's the original price?
5. If $ a + b = c $, and $ a = 5 $, $ c = 12 $, what is $ b $?

**Tip:** Always double-check your solution by substituting the variable back into the original equation to verify its correctness.

Solve one-step equations and simplify expressions from a worksheet.

This page provides step-by-step solutions for solving one-step equations like x + 12 = 7 and simplifying algebraic expressions such as 4x + 9 - 6x - y. Ideal for middle school students (Grades 6-8).

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