① One-step equations
Solve using a single inverse operation — add, subtract, multiply or divide.
② Two-step equations
Two operations needed: undo the addition or subtraction first, then the multiplication.
③ Other equation forms
Equations that don't fit the usual pattern — a fraction coefficient, or \(x\) being subtracted.
④ Two-step — extending
Larger numbers, negative answers, x on right, decimal solutions.
⑤ Equations — unknowns on both sides
Collect the unknown terms on one side first.
⑥ Equations with brackets
Expand the brackets first, then solve.
⑦ Forming equations — perimeters
Use the perimeter formula to write and solve an equation.
⑧ Forming equations — areas
Use the area formula to write and solve an equation.
Key steps
Golden rule: whatever you do to one side, do to the other.
Two-step: undo addition/subtraction first, then multiplication/division.
Both sides: move the smaller \(x\) term across first.
Brackets: expand first, then solve. Check signs carefully.
Shapes: write the formula, substitute the expressions, simplify, solve.