Forming and Solving Equations

GCSE Edexcel | Foundation & Higher

Learning Objectives

• Understand what it means to form an equation
• Translate word problems into algebraic equations
• Solve linear equations accurately
• Check answers in context

🎥 Video Explanation

1️⃣ What Does Forming an Equation Mean?

Forming an equation means using a letter (usually x) to represent an unknown value and then writing a mathematical sentence that represents the information given in words.

Example: Let the number be x.

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(Word problem → algebra diagram)

2️⃣ Translating Words into Maths

3️⃣ Example 1 – Basic Equation

Question: A number is multiplied by 4 and then 7 is added. The result is 31.

Forming the equation:

Let the number be x

4x + 7 = 31

Solving:

4x = 24

x = 6

4️⃣ Example 2 – Money Problem

Question: Sam buys 3 pens and a notebook costing £2. The total cost is £11.

Equation: 3x + 2 = 11

Solution: x = 3

5️⃣ Example 3 – Age Problem

Question: Aisha is 5 years older than Ben. The sum of their ages is 27.

Equation: x + (x + 5) = 27

Solution: x = 11

📝 Practice Questions

1. A number is doubled and then reduced by 9 to give 15.
2. The perimeter of a square is 36 cm. Find the length of one side.
3. The sum of three consecutive numbers is 72.
4. A phone costs £x. A case costs £5 less. Together they cost £35.