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Maths Lab · Free lesson · 20 minutes

Solve an equation without losing the balance

Translate a word sentence into an equation, preserve equality through inverse operations and verify a solution.

JSS1 · equations

01 · Think first

Start with a question.

Three identical notebooks and a ₦200 delivery charge cost ₦1,100. A useful equation separates what repeats from what happens once.

What you already know
  • Multiply and divide integers
  • Recognise inverse operations
  • Read 3x as three times x
For 3x + 5 = 20, which first operation keeps the equation balanced?

02 · See it

Undo the operations in reverse order

Both sides change equally. The arrows show equivalent equations, each with the same solution.

Original
3x + 5 = 20
Subtract 5 on both sides
3x = 15
Divide both sides by 3
x = 5
Substitution check
3(5) + 5 = 20

Use the justified worked steps below to explore this idea.

03 · Show steps · explain why

One justified step at a time.

  1. 1

    'Three more than twice a number is 17' → 2n + 3 = 17

    Twice a number is 2n; three more adds 3. The word 'is' makes an equality.

04 · Mistake clinic

Find the first wrong idea.

Tempting wrong line

3x + 5 = 20 → x = 20/3 − 5.

Compare the correction and its reason

3x = 20 − 5, so x = (20 − 5)/3 = 5.

The wrong operation divides the total before removing the added 5. A correct division first would divide every term: x + 5/3 = 20/3.

Check: Substitute the proposed answer into the original equation. Does it really make the two sides equal?

A mistake is evidence about the next idea to repair. It is not a label for the learner.

05 · Your turn

Try first. Then use a hint.

1. Solve 4x + 6 = 30. Enter x.guided practice
2. Solve 9 − 2x = −5. Enter x.independent practice
3. Four identical tickets plus a ₦300 booking fee cost ₦2,700. Find one ticket's price in naira.far practice

06 · Check & reflect → next step

Understanding includes explaining.

Explain one operation using equality rather than saying 'move it across'. What did your substitution check prove?

Choose your next learning need

When one equation has two unknowns, it may have many solutions. Learn how a second independent equation identifies a common solution.

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Source and review status

JEM-J1-M04-002 · Phase 3A JSS1 Mathematics REPAIRED · Lesson 8 · printed pp. 23–24

This published free lesson contains selected explanations and authored practice. Complete canonical volumes and tutor solutions remain in the protected Content Vault.