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Solving Equations

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Linear Equations

A linear equation contains an unknown raised to the power of 1. To solve, isolate the unknown by performing inverse operations on both sides. Always do the same operation to both sides to keep the equation balanced.

Equations with Brackets

Expand brackets first, then collect like terms and solve. For example: 3(x + 2) = 15 → 3x + 6 = 15 → 3x = 9 → x = 3.

Equations with Fractions

Multiply every term by the lowest common denominator (LCD) to eliminate fractions, then solve normally.

Quadratic Equations

A quadratic equation has the form ax² + bx + c = 0. Solve by factorising, using the quadratic formula, or completing the square.

x = (−b ± √(b² − 4ac)) / 2a

Key Points

  • Always perform the same operation on both sides
  • Expand brackets before collecting like terms
  • For quadratics: try factorising first, then use the formula
  • Check your answer by substituting back into the original equation

Exam Tips

  • Show every step of your working — marks are awarded for method
  • If the question says "solve", you must find the value(s) of x
  • For quadratics, remember there can be 0, 1, or 2 solutions