A5AlgebraFoundation

Linear Equations

Solving an equation means finding the value of the letter that makes it true. The golden rule is balance: whatever you do to one side, you must do to the other.

40 min Video by Maths Genie AQA GCSE Maths

Solving EquationsWatch the walkthrough, then read the notes below.

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What you'll learn

Solve one- and two-step equations
Solve equations with brackets
Solve equations with the unknown on both sides
Check a solution by substituting back

Keeping it balanced

Use inverse operations to get the letter on its own. Inverse of $+$ is $-$ , inverse of $\times$ is $\div$ . Do the same thing to both sides every step.

1Subtract 5 from both sides:

3 x = 15

2Divide both sides by 3:

x = 5

Answer

x = 5

Unknowns on both sides

When the letter appears on both sides, move all the letter terms to one side and the numbers to the other, then solve as usual.

1Subtract

3 x

2 x - 2 = 8

2Add 2:

2 x = 10

3Divide by 2:

x = 5

Answer

x = 5

Tip — Always check: put your answer back into the original equation and see if both sides match.

Remember these

do the same to both sides

The balance rule.

+ \leftrightarrow -, \times \leftrightarrow \div

Inverse operations.

Watch out for these

Only changing one side of the equation.

Apply each step to both sides to keep it balanced.

Dividing before dealing with the +/− term.

Undo addition/subtraction first, then divide.

Key takeaways

Use inverse operations to isolate the letter.
Do the same to both sides every step.
Move letters to one side when they appear on both.

Test yourself

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