Cracking the Code: Solving Linear Equations

Imagine a safe with a secret number locked inside. You know a clue: when you multiply the number by 3 and then add 5, you get 20. How do you work backwards to find the number? This is exactly what solving an equation means — you are a detective, reversing operations to uncover a hidden value. Before the main lesson, try to recall: what is the opposite (inverse) of addition? What is the inverse of multiplication?

A linear equation is a mathematical statement that says two expressions are equal, and the unknown value appears only to the power of 1 (never squared or cubed). The unknown is called the variable, and it is usually written as a letter such as x. For example: 3x + 5 = 20 Here, x is the variable, and the equation tells you that three times x, plus 5, equals 20. To solve the equation, your goal is to isolate the variable — get x on its own on one side of the equals sign. You do this by performing inverse operations: the opposite of each operation applied to x, in reverse order. The golden rule: whatever you do to one side of the equation, you MUST do the same to the other side. This keeps the equation balanced, like a set of scales. Inverse operation pairs to remember: • Addition ↔ Subtraction • Multiplication ↔ Division Step-by-step strategy: 1. Identify what has been done to x (reading the equation carefully). 2. Undo the last operation first (work in reverse order — BIDMAS in reverse). 3. Repeat until x is isolated. 4. Check: substitute your answer back into the original equation to confirm both sides are equal.