Linear equations 1 Revision Notes for Edexcel GCSE Maths

Linear equations 1

What is an equation?

An equation is like a pair of balanced scales. The equals sign (=) shows that both sides have the same value, just like scales that are perfectly balanced.

The letter in an equation represents an unknown number that we need to find. This letter is called a variable. When we solve the equation, we work out what number the letter represents.

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Think of it this way: if you have scales with some weights, and you know the total weight on each side is the same, you can work out what the unknown weight must be. This analogy helps visualise why we need to keep equations balanced when solving them.

How to solve linear equations

The main goal when solving any linear equation is to get the variable on its own on one side of the equation.

Key principle

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Whatever you do to one side of the equation, you must do the same thing to the other side. This keeps the equation balanced, just like keeping scales level.

Steps to follow

Step 1: Write down the equation clearly

Step 2: Decide what operations you need to "undo" to isolate the variable

Step 3: Apply the inverse operation to both sides:

If the variable has a number added, subtract that number from both sides
If the variable has a number subtracted, add that number to both sides
If the variable is multiplied by a number, divide both sides by that number
If the variable is divided by a number, multiply both sides by that number

Step 4: Write your working neatly:

Start a new line for each step
Include an equals sign on every line
Do only one operation at a time
Write what operation you're doing in brackets

Worked examples

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Worked Example 1: Solving Addition Equations

Solve $m + 6 = 15$

m + 6 = 15    (subtract 6 from both sides)
m = 9

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Worked Example 2: Solving Multiplication Equations

Solve $8p = 36$

8p = 36       (divide both sides by 8)
p = 4.5

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Worked Example 3: Solving Two-Step Equations

Solve $5x + 3 = 18$

5x + 3 = 18   (subtract 3 from both sides)
5x = 15       (divide both sides by 5)
x = 3

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Worked Example 4: Solving Equations with Subtraction

Solve $2a - 7 = 11$

2a - 7 = 11   (add 7 to both sides)
2a = 18       (divide both sides by 2)
a = 9

Important tips for exams

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Exam Success Tips:

Show every step of your working - you can get marks for method even if your final answer is wrong
Check your answer by substituting it back into the original equation
Remember that fractions and decimals can be valid answers
Take your time with two-step equations - do one operation at a time

Remember!

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Key Points to Remember:

An equation is like balanced scales - whatever you do to one side, do to the other
The goal is to isolate the variable on one side of the equation
Use inverse operations to "undo" what's been done to the variable
Show your working clearly with one step per line and an equals sign on every line
Check your answer by substituting it back into the original equation

Linear equations 1 (Edexcel GCSE Maths): Revision Notes