Forming Equations

Translate words into algebra: "a number" = x, "three more" = + 3, "twice" = 2x.

Example: "I think of a number, double it and add 5. The answer is 17." 2x + 5 = 17

Solving (2 Steps)

Use inverse operations to find x. Do the addition/subtraction first!

Example: 2x + 5 = 17 2x = 12 x = 6

Variable on Both Sides

Collect all x terms on one side (the side with more x) and numbers on the other.

Example: 5x + 3 = 2x + 12 3x + 3 = 12 3x = 9 → x = 3

Equations with Brackets

Expand the brackets first, then solve as normal.

Example: 3(x + 4) = 18 3x + 12 = 18 3x = 6 → x = 2

Balancing Method

Whatever you do to one side, you MUST do to the other side to keep it equal.

Equations from Shapes

Use properties like "angles in a triangle = 180°" to form equations.

Example: Angles: x, 2x, 3x x + 2x + 3x = 180 6x = 180 x = 30

Equations with Fractions

Multiply through by the common denominator to clear all fractions.

Example: x/3 + x/2 = 10 Multiply by 6: 2x + 3x = 60 5x = 60 → x = 12

Solving Quadratics by Factorising

Set the equation to zero, factorise, then find the x values that make each bracket zero.

Formula: (x+p)(x+q) = 0 → x = -p or x = -q

Example: x² - 5x + 6 = 0 (x-2)(x-3) = 0 → x=2 or x=3

The Quadratic Formula

Used when you can't factorise. Always round to given accuracy.

Formula: x = [-b ± √(b² - 4ac)] / 2a

Iterative Methods

Use a formula repeatedly to find increasingly accurate approximations for a root.