Key Concepts:
- Combining Like Terms: Example: (2x + 3x = 5x)
- Distributive Property: Expanding expressions like (2(x + 3) = 2x + 6).
- Variables on Both Sides: Move terms across the equation before solving.
Skills Covered:
- Solving equations by applying inverse operations (addition, subtraction, multiplication, division).
- Solving equations with variables on both sides.
- Checking solutions by substituting values back into the original equation.
Example Problems:
- Solve: (2x + 3 = 3x - 5)
- Subtract (2x) from both sides: (3 = x - 5)
- Add 5 to both sides: (x = 8)
- Solve: (4(2x - 1) = 3x + 5)
- Distribute: (8x - 4 = 3x + 5)
- Subtract (3x) from both sides: (5x - 4 = 5)
- Add 4 to both sides: (5x = 9)
- Divide by 5: (x = \frac{9}{5})