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Mathematics · Grades 8–11

Find the mistake: algebra

Apply the same valid operation to both sides and respect restrictions such as division by zero.

Make a worksheet

Understand the idea

Keep equations balanced

Apply the same valid operation to both sides and respect restrictions such as division by zero.

Check by substitution

Substituting a proposed solution into the original equation can expose an error.

Examples and reasoning

A pupil expands 3(x + 4) as 3x + 4. Correct it.

3x + 12. The factor 3 multiplies both terms.

3x + 12. The factor 3 multiplies both terms.

A pupil says (x + 5)² = x² + 25. What is missing?

The middle term 10x is missing: (x + 5)² = x² + 10x + 25.

The middle term 10x is missing: (x + 5)² = x² + 10x + 25.

Check your understanding

  1. A pupil combines 2x + 3x² as 5x³. Explain the error.

  2. Solve 4x − 7 = 21.

  3. Solve 5x + 2 = 3x + 18.

  4. Solving −2x > 6 gives

    1. x < 3
    2. x < −3
    3. x > −3
    4. x > 3

Answers and marking notes

Answers and marking notes
  1. x and x² are unlike terms and cannot be added by adding exponents; the expression remains 3x² + 2x.

    x and x² are unlike terms and cannot be added by adding exponents; the expression remains 3x² + 2x.

  2. 7

    4x = 28, so x = 7.

  3. 8

    2x = 16, so x = 8.

  4. x < −3

    x < −3

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.

Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.