Solving equations: the basics

In short: An equation says that two terms are equal. You solve it by applying the same operations to both sides until the unknown stands alone.

In more detail: The balance picture helps: whatever you do on one side you must do on the other.

In detail

• Example: 2x + 3 = 11. First subtract 3: 2x = 8. Then divide by 2: x = 4.
• Check: Insert x = 4: 2·4 + 3 = 11 is correct.
• Brackets: Multiply out first: 2(x + 1) = 2x + 2.
• Unknown on both sides: Bring to one side: 3x + 1 = x + 7 → 2x = 6 → x = 3.
• Quadratic equations: x² − 5x + 6 = 0 → (x − 2)(x − 3) = 0 → x = 2 or x = 3.
• Solution formula: x = (−b ± √(b² − 4ac)) / 2a.
• Word problems: Name the unknown, set up the equation, solve, check the answer.
• Connection: Helps with rule of three and percentages (bruchrechnung-grundlagen).