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Subject
Meaning: Isolate the requested variable; preserve the relation
Balance: Undo in reverse on BOTH sides; a = (v−u)/t, t ≠ 0
Several steps
Brackets: P = 2(l+w) → l = P/2−w
Roots: r = √(A/π); geometrical lengths are positive
Both signs: Higher: y = x²+4 → x = ±√(y−4), y ≥ 4
Models
Charges: Fixed fee + variable cost; £22 taxi fare → 10 km
Check: Use consistent units; substitute into original relation
Repeated subject
Collect / factor: Higher: y = ax+bx → x = y/(a+b), a+b ≠ 0
Fractional formula: Higher: y = (3x+2)/(x−1) → x = (y+2)/(y−3)
Domain: Higher: Record zero-denominator and root restrictions
Connections
Subject → Several steps: Inverse operations isolate a formula subject
