Mathematics • Year 7 • Unit 2 • Lesson 13
One-Step Multiply/Divide — Mixed Challenge
Mix it up: solve six equations of varied form, find a classic inverse-operation mistake, then design equations that share the same solution.
1. Mixed problems — choose the right inverse
For each: identify the operation on x, then apply its inverse to BOTH sides. Always check. 2 marks each
1.1 Solve 6x = −42.
1.2 Solve x⁄(−4) = 5.
1.3 Solve −2x = 18.
1.4 Solve x⁄(−3) = −6. (Two negatives.)
1.5 Solve 9x = 0. (What's the only value of x that works?)
1.6 Solve 4x = 30. (Answer is a fraction or decimal — leave as a simplified fraction OR write to one decimal place.)
2. Find the mistake
Another Year 7 student has tried to solve x⁄3 = 9. Their working is shown below. Exactly one line contains a mistake. Spot it, explain why it's wrong, then redo the solve correctly. 3 marks
Student's working — Solve x⁄3 = 9:
Line 1: x is being divided by 3.
Line 2: The inverse of ÷3 is also ÷3, so divide both sides by 3.
Line 3: (x⁄3) ÷ 3 = 9 ÷ 3
Line 4: x = 3.
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Redo the working correctly, including a check.
Stuck? The inverse of ÷3 is ×3 (NOT another ÷3). Multiply both sides by 3 to get x = 27.3. Open-ended challenge — design your own equations
This question has more than one correct answer. Show one that works and explain. 4 marks
3.1 Design THREE different one-step equations (one with × and positive coefficient, one with × and NEGATIVE coefficient, one with ÷) that ALL have the same solution: x = −4.
For each equation, show:
(i) the equation itself,
(ii) the inverse operation you'd use to solve it,
(iii) a substitution check that x = −4 really works.
Bonus: Write a short real-world story for ONE of your equations.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — 6x = −42
Divide both sides by 6: x = −42 ÷ 6 = −7. Check: 6 × (−7) = −42 ✓.
1.2 — x⁄(−4) = 5
Multiply both sides by −4: x = 5 × (−4) = −20. Check: −20 ÷ (−4) = 5 ✓.
1.3 — −2x = 18
Divide both sides by −2: x = 18 ÷ (−2) = −9. Check: −2 × (−9) = 18 ✓.
1.4 — x⁄(−3) = −6
Multiply both sides by −3: x = (−6) × (−3) = 18. Check: 18 ÷ (−3) = −6 ✓.
1.5 — 9x = 0
Divide both sides by 9: x = 0 ÷ 9 = 0. (Anything times 0 is 0, so x must be 0.) Check: 9 × 0 = 0 ✓.
1.6 — 4x = 30
Divide both sides by 4: x = 30 ÷ 4 = 7.5 (or equivalently 15⁄2). Check: 4 × 7.5 = 30 ✓.
2 — Find the mistake
(a) The mistake is on Line 2.
(b) The inverse of division is multiplication, not another division. To undo "÷3", we multiply by 3.
(c) Corrected working: x⁄3 = 9 → multiply both sides by 3 → x = 9 × 3 = 27. Check: 27 ÷ 3 = 9 ✓.
3 — Open-ended (sample solutions)
Three valid equations with solution x = −4:
(a) 3x = −12 — divide by 3. Check: 3 × (−4) = −12 ✓.
(b) −5x = 20 — divide by −5. Check: −5 × (−4) = 20 ✓.
(c) x⁄2 = −2 — multiply by 2. Check: (−4) ÷ 2 = −2 ✓.
Story example (for −5x = 20): "A submarine is descending at 5 m per minute (call this −5 m/min). After x minutes, it has moved a total of −20 m (i.e. 20 m down). How many minutes have passed? Answer: x = −4 isn't physical here — pick a story that makes negative time meaningful, e.g. 'temperature drop' as in worksheet 2."
Marking: 1 mark per valid equation (×3); 1 mark for a sensible real-world story.