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.
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.