1. Let's start with a common GCSE math problem: solving a linear equation. 2. Problem: Solve for $x$ in the equation $3x + 5 = 20$. 3. Formula and rules: To solve linear equations, we isolate $x$ by performing inverse operations. 4. Step 1: Subtract 5 from both sides: $$3x + 5 - 5 = 20 - 5$$ $$3x = 15$$ 5. Step 2: Divide both sides by 3: $$\frac{3x}{3} = \frac{15}{3}$$ $$x = 5$$ 6. Explanation: We first removed the constant term by subtracting 5, then divided by the coefficient of $x$ to isolate it. 7. Final answer: $x = 5$. This type of problem is very common in GCSE math exams and practicing it helps build confidence.