Linear equations 2 Revision Notes for Edexcel GCSE Maths

Linear equations 2

Equations with brackets

Linear equations with brackets are equations that contain terms like 2(3y + 5) or 5(p - 4). To solve these equations effectively, you need to follow a systematic approach.

Always start by expanding the brackets first, then collect like terms together. This means you multiply the number outside the brackets by everything inside the brackets before attempting to solve the equation.

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When working with brackets in linear equations, think of the number outside as being distributed to every term inside the brackets. This distributive property is fundamental to solving these types of equations correctly.

Method for solving equations with brackets

When you see an equation with brackets, follow these steps:

Step 1: Expand the brackets by multiplying out
Step 2: Collect like terms on each side
Step 3: Use inverse operations to solve
Step 4: Do one operation at a time and write down what you're doing at each step

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Worked Example: Solving with Brackets

Let's solve: 2(3y + 5) = 22

Step 1: Expand the brackets: 2 × 3y = 6y and 2 × 5 = 10

Step 2: This gives us: 6y + 10 = 22

Step 3: Subtract 10 from both sides: 6y = 12

Step 4: Divide both sides by 6: y = 2

Equations with the letter on both sides

Equations with variables on both sides occur when the unknown letter appears on both the left and right sides of the equation. To solve these, you need to collect all the letter terms on one side and all the number terms on the other side.

Method for equations with variables on both sides

The key principle is to get the letter on its own on one side of the equation. You do this by collecting like terms so that all the variables end up together.

Step 1: Add or subtract multiples of the variable to get all letter terms on one side
Step 2: Add or subtract numbers to get all number terms on the other side
Step 3: Remember to do the same operation to both sides of the equation
Step 4: Divide or multiply to find the value of the variable

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Worked Example: Variables on Both Sides

Let's solve: 4x + 26 = 2 - 2x

Step 1: Add 2x to both sides: 6x + 26 = 2

Step 2: Subtract 26 from both sides: 6x = -24

Step 3: Divide both sides by 6: x = -4

Worked examples

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Worked Example 1: Expanding Brackets and Subtracting

Solve: 7p + 2 = 5(p - 4)

Step 1: Expand the brackets on the right side 7p + 2 = 5p - 20

Step 2: Subtract 5p from both sides to collect p terms 2p + 2 = -20

Step 3: Subtract 2 from both sides 2p = -22

Step 4: Divide both sides by 2 p = -11

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Worked Example 2: Equations with Fractions

Solve: $\frac{10 - y}{5} = 3$

Step 1: Multiply both sides by 5 to remove the fraction 10 - y = 15

Step 2: Add y to both sides 10 = 15 + y

Step 3: Subtract 15 from both sides -5 = y

You can write your answer as y = -5. As long as the letter is on its own on one side, the equation is solved.

Exam tips

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Critical Exam Strategies:

Don't use trial methods to solve equations - you won't get method marks and probably won't find the correct answer
When you have a positive coefficient (like +5x), it's often easier to work with by adding the variable term to both sides
Start by expanding brackets then group all the variable terms on one side
Show your working clearly - write down each operation you perform

Practice questions

These questions appear at different target grades:

Target Grade 3:

Solve 33 - 5x = 8
Solve 4 - 6x = 5 - 8x

Target Grade 4:

Solve 3r - 7 = 5r + 15
Solve 2(4h + 3) = 2
Solve 3y + 19 = 5(y - 2)
Solve $\frac{16 - 5m}{3} = 7$

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Key Points to Remember:

Always expand brackets first before attempting to solve the equation
Do one operation at a time and show each step clearly in your working
Perform the same operation to both sides to keep the equation balanced
Collect like terms to get all variables on one side and all numbers on the other
Don't use trial and error methods - use systematic algebraic methods for full marks

Linear equations 2 (Edexcel GCSE Maths): Revision Notes