Solution:
1. Given equation:
- 0.5(4x + 24) = 22x - 2
2. Simplify the left side:
- Apply the distributive property: 0.5 \times 4x + 0.5 \times 24 = 22x - 2
- This gives us: 2x + 12 = 22x - 2
3. Rearrange to solve for x:
- Subtract 2x from both sides: 2x + 12 - 2x = 22x - 2 - 2x
- Simplify: 12 = 20x - 2
4. Add 2 to both sides to isolate terms:
- 12 + 2 = 20x - 2 + 2
- Simplify: 14 = 20x
5. Divide by 20 to solve for x:
- x = \frac{14}{20}
- Simplify the fraction: x = \frac{7}{10}
The solution to the equation is $x = \\frac{7}{10}$.