# Algebraic equations

- Simple example:
- Start with equation \(x + 9 = 12\)
- Subtract 9 from both sides, so you are left with \(x = 3\)

- More complex example:
- Start with equation \(15 - 2x = 7\)
- Subtract 15 from both sides, so you have \(-2x = -8\)
- Divide both side by -2, you are left with \(x = 4\)

- Example with fractions:
- Start with equation \(\frac{x}{5} = 20\)
- Multiply both sides by 5, so you are left with \(x = 100\)

- Example with rearranging:
- Start with equation \(3 = \frac{36}{x}\)
- Multiple both sides with \(x\), so you have \(3x = 36\)
- Divide both sides by 3, so you are left with \(x = 12\)

- Example with expansion:
- Start with equation \(8(x + 2) = 36\)
- Expand the equation, so you have \(8x + 16 = 26\)
- Subtract 16 from both sides, so you have \(8x = 20\)
- Divide both sides by 8, so you are left with \(x = 2.5\)