algebra
Solving Linear Equations
The Golden Rule
Whatever you do to one side, do to the other side!
The 4-Step Method
1
Simplify both sides
Combine like terms, distribute if needed
2
Move variables to one side
Use addition/subtraction
3
Move constants to the other side
Use addition/subtraction
4
Isolate the variable
Divide by the coefficient
Examples
2x + 5 = 13x = 42x = 8 → x = 4
3x - 7 = 2x + 5x = 12x = 12
4(x - 2) = 20x = 74x - 8 = 20 → 4x = 28
💡Check Your Answer
Always plug your answer back into the original equation to verify! For 2x + 5 = 13: plug in x = 4 → 2(4) + 5 = 8 + 5 = 13 ✓
⚠️ Watch Out For
- Sign changes when moving terms across the equals sign
- Distributing negatives properly: -(x + 2) = -x - 2
- Dividing both sides by the coefficient, not just one side