Mathematics • Year 7 • Unit 2 • Lesson 11
What is an Equation? — Mixed Challenge
Pull everything together: sort expressions from equations, identify LHS/RHS, write equations from English, check solutions, find a classic substitution mistake, and finish with an open-ended equation-build.
1. Mixed problems — choose the right idea
Each question uses a different idea from Lesson 11. Show your working. 2 marks each
1.1 Classify each as an expression or an equation: (a) 2x + 7 = 11 (b) 5a − 2b + 4 (c) x² + 3x (d) y = 5.
1.2 For the equation 2x + 11 = 5x − 4, write down (a) the LHS and (b) the RHS.
1.3 Write an equation for: "Three times a number, decreased by 4, equals 11." Use x for the number.
1.4 Check whether x = 6 is a solution of 2x − 5 = 7. Show LHS, RHS and the conclusion.
1.5 Write an equation for: "Five more than twice a number is equal to twenty-one." Then identify the LHS and the RHS.
1.6 Two of the values below are solutions of x² = 9, and the other two are not. Test all four by substitution and circle the ones that work: x = 3, x = −3, x = 9, x = 1.
2. Find the mistake
Another Year 7 student has tried to check whether x = 5 is a solution of 3x + 2 = 17. Their working is shown below. Exactly one line contains a mistake. Spot it, explain why it's wrong, then redo the check correctly. 3 marks
Student's working — Is x = 5 a solution of 3x + 2 = 17?
Line 1: LHS = 3x + 2 | RHS = 17
Line 2: Substitute x = 5: LHS = 3 + 5 + 2 = 10
Line 3: LHS = 10 , RHS = 17 → LHS ≠ RHS
Line 4: Conclusion: x = 5 is NOT a solution.
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Redo the substitution correctly, then write the corrected conclusion.
Stuck? In 3x, the 3 and the x are multiplied (3x means 3 × x), not added.3. Open-ended challenge — build your own equation
This question has more than one correct answer. Show one that works and explain. 4 marks
3.1 Write an equation that satisfies ALL of the following rules:
(i) the LHS contains the variable x with a coefficient of 4
(ii) the LHS also contains a constant term (a plain number)
(iii) the RHS is a single number (no x)
(iv) the solution is x = 5 — that is, substituting x = 5 must make LHS = RHS.
Write down your equation, check that x = 5 really works by substituting, then briefly explain in one or two sentences how each rule is satisfied.
Bonus: Write a short real-world story (one sentence) that your equation could describe.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Expression or equation?
(a) 2x + 7 = 11 → equation. (b) 5a − 2b + 4 → expression. (c) x² + 3x → expression. (d) y = 5 → equation (it has =).
1.2 — LHS and RHS of 2x + 11 = 5x − 4
(a) LHS = 2x + 11. (b) RHS = 5x − 4. (Yes, the RHS can contain a variable too.)
1.3 — "Three times a number, decreased by 4, equals 11"
3x − 4 = 11. "Three times a number" = 3x; "decreased by 4" = − 4; "equals 11" = = 11.
1.4 — Check x = 6 in 2x − 5 = 7
LHS = 2(6) − 5 = 12 − 5 = 7. RHS = 7. LHS = RHS ✓. Yes, x = 6 is the solution.
1.5 — "Five more than twice a number equals twenty-one"
Equation: 2x + 5 = 21. LHS = 2x + 5; RHS = 21. (You can also write 5 + 2x = 21; same thing.)
1.6 — Which values satisfy x² = 9?
x = 3: 3² = 9 ✓. x = −3: (−3)² = 9 ✓. x = 9: 9² = 81 ≠ 9 ✗. x = 1: 1² = 1 ≠ 9 ✗. The two solutions are x = 3 and x = −3.
2 — Find the mistake
(a) The mistake is on Line 2.
(b) The student treated 3x as "3 + x" instead of "3 × x". In algebra, a number written next to a letter means multiplication, not addition.
(c) Corrected substitution: LHS = 3(5) + 2 = 15 + 2 = 17. RHS = 17. LHS = RHS ✓. Therefore x = 5 IS a solution of 3x + 2 = 17.
3 — Open-ended (sample solutions)
Example equation: 4x + 3 = 23. Rule check: (i) coefficient of x on LHS is 4 ✓; (ii) constant term on LHS is +3 ✓; (iii) RHS is the single number 23 ✓; (iv) substitute x = 5: LHS = 4(5) + 3 = 20 + 3 = 23 = RHS ✓.
Other valid examples: 4x − 1 = 19, 4x + 10 = 30, 4x + 0 = 20 (which we'd just write as 4x = 20).
Story: "I bought 5 packs of trading cards at $4 each plus a $3 folder, and spent $23 in total — x is the number of packs."
Marking: 2 for a valid equation matching all rules; 1 for the substitution check; 1 for a sensible story.