Mathematics • Year 7 • Unit 2 • Lesson 12

One-Step Add/Subtract — Mixed Challenge

Mix it up: solve six one-step equations of varied difficulty, find a classic balance-rule mistake, then design an equation to fit a fixed solution.

Master · Mixed Challenge

1. Mixed problems — choose the right inverse

For each: identify what is being done to x, then apply the inverse to BOTH sides. Always check. 2 marks each

1.1 Solve x + 8 = 23.

1.2 Solve x − 13 = 4.

1.3 Solve −2 = x − 8.

1.4 Solve x + 0.75 = 2.25.

1.5 Solve x − 1.5 = −4.5. (Two negatives — read carefully.)

1.6 Solve x + (−3) = 10. (Adding a negative is the same as subtracting.)

Stuck on 1.6? x + (−3) is just x − 3. Then add 3 to both sides.

2. Find the mistake

Another Year 7 student has tried to solve x + 6 = 14. 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 + 6 = 14:

Line 1: x has +6 added to it, so the inverse is −6.

Line 2: x + 6 − 6 = 14

Line 3: x = 14

Line 4: Check: 14 + 6 = 20, not 14. Hmm, didn't work — but I'll write x = 14 anyway.

(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? Whatever you do to one side of an equation, you must do to the OTHER side too. The student subtracted 6 from the left only.

3. Open-ended challenge — design your own equation

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 using +, one using −, and one with a decimal) that ALL have the same solution: x = 7.

For each equation, show:
(i) the equation itself,
(ii) the inverse operation you'd use,
(iii) a substitution check that x = 7 really works.

Bonus: Write a short real-world story for ONE of your equations.

Stuck? Start with x = 7. Now add 4 to both sides → x + 4 = 11. That's a valid equation. Try the same trick with subtraction and a decimal.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

1.1 — x + 8 = 23

Subtract 8 from both sides: x = 23 − 8 = 15. Check: 15 + 8 = 23 ✓.

1.2 — x − 13 = 4

Add 13 to both sides: x = 4 + 13 = 17. Check: 17 − 13 = 4 ✓.

1.3 — −2 = x − 8

Add 8 to both sides: −2 + 8 = x, so x = 6. Check: 6 − 8 = −2 ✓.

1.4 — x + 0.75 = 2.25

Subtract 0.75 from both sides: x = 2.25 − 0.75 = 1.5. Check: 1.5 + 0.75 = 2.25 ✓.

1.5 — x − 1.5 = −4.5

Add 1.5 to both sides: x = −4.5 + 1.5 = −3. Check: −3 − 1.5 = −4.5 ✓.

1.6 — x + (−3) = 10

Rewrite as x − 3 = 10. Add 3 to both sides: x = 10 + 3 = 13. Check: 13 + (−3) = 10 ✓.

2 — Find the mistake

(a) The mistake is on Line 2.
(b) The student subtracted 6 from the LHS only, breaking the balance. They needed to subtract 6 from the RIGHT side too: 14 − 6 = 8.
(c) Corrected working: x + 6 − 6 = 14 − 6 → x = 8. Check: 8 + 6 = 14 ✓ — now it balances.

3 — Open-ended (sample solutions)

Three valid equations with solution x = 7:
(a) x + 4 = 11. Inverse: subtract 4. Check: 7 + 4 = 11 ✓.
(b) x − 5 = 2. Inverse: add 5. Check: 7 − 5 = 2 ✓.
(c) x + 1.5 = 8.5. Inverse: subtract 1.5. Check: 7 + 1.5 = 8.5 ✓.
Story example: "I had x dollars. I earned $4 babysitting and now have $11. How much did I start with?"

Marking: 1 mark per valid equation (×3); 1 mark for a sensible real-world story.