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MathematicsGrade 925 min

Algebra: Solving Linear Equations

Solve linear equations step by step using the balance method — and check every answer.

What is algebra?

Algebra uses letters for unknown numbers: x + 3 = 7. Solving the equation means finding the value of x.

The golden rule

Whatever you do to one side, do to the other — keep the equation balanced, like a scale.

Solving step by step

Solve 3x + 5 = 20:

  1. Subtract 5 from both sides: 3x = 15
  2. Divide both sides by 3: x = 5

With x on both sides

Solve 5x − 2 = 2x + 10:

  1. Subtract 2x: 3x − 2 = 10
  2. Add 2: 3x = 12
  3. Divide by 3: x = 4

Brackets

3(x + 2) = 18 → divide both sides by 3 → x + 2 = 6 → x = 4.

Check your answer

Always substitute back: 3x + 5 = 20 with x = 5 gives 3(5) + 5 = 20 ✓ Correct!

Practise

  1. 4x − 7 = 21
  2. 2(x + 3) = 16
  3. 6x − 4 = 2x + 12

Follow along (device voice)

Listen and follow along as each word is spoken

What is algebra? Algebra uses letters for unknown numbers: x + 3 = 7. Solving the equation means finding the value of x. The golden rule Whatever you do to one side, do to the other — keep the equation balanced, like a scale. Solving step by step Solve 3x + 5 = 20: 1. Subtract 5 from both sides: 3x = 15 2. Divide both sides by 3: x = 5 With x on both sides Solve 5x − 2 = 2x + 10: 1. Subtract 2x: 3x − 2 = 10 2. Add 2: 3x = 12 3. Divide by 3: x = 4 Brackets 3 x + 2 = 18 → divide both sides by 3 → x + 2 = 6 → x = 4. Check your answer Always substitute back: 3x + 5 = 20 with x = 5 gives 3 5 + 5 = 20 ✓ Correct Practise 1. 4x − 7 = 21 2. 2 x + 3 = 16 3. 6x − 4 = 2x + 12