Mathematics • Year 7 • Unit 2 • Lesson 11
What is an Equation?
Build the basics: tell expressions from equations, name the LHS and RHS, and use substitution to check whether a value is a solution.
1. I do — fully worked example
Read every line. Each step has a short reason on the right so you can see why, not just what.
Problem. Is x = 4 a solution of 5x − 3 = 17?
Step 1 — Identify the LHS and RHS.
LHS = 5x − 3 | RHS = 17
Reason: the equals sign splits the equation. Everything to the left is the LHS; everything to the right is the RHS.
Step 2 — Substitute x = 4 into the LHS.
LHS = 5(4) − 3 = 20 − 3 = 17
Reason: replace every x with the value 4, then use order of operations — multiplication before subtraction.
Step 3 — Compare LHS with RHS.
LHS = 17 and RHS = 17 → LHS = RHS ✓
Reason: the scales are level — both pans hold 17. The value satisfies the equation.
Step 4 — Write the conclusion.
Therefore x = 4 IS a solution of 5x − 3 = 17.
Answer: Yes, x = 4 is a solution because substituting gives LHS = RHS = 17.
2. We do — fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank line. 4 marks
Problem. Is x = 6 a solution of 2x − 5 = 7?
Step 1 — Identify LHS and RHS:
LHS = _______ | RHS = _______
Step 2 — Substitute x = 6 into the LHS:
LHS = 2(____) − 5 = _____ − 5 = _____
Step 3 — Compare LHS and RHS:
LHS = ____ , RHS = ____ → LHS ____ RHS (tick or cross)
Step 4 — Conclusion:
Therefore x = 6 _______________________ a solution.
3. You do — independent practice
Show your working under each question. The first four are foundation, the middle two are standard, and the last two are extension.
Foundation — one idea at a time
3.1 State whether each is an expression or an equation. (a) 3x + 7 (b) 3x + 7 = 19 (c) y² = 16 1 mark
3.2 For the equation 4x − 3 = 9, what is the LHS and what is the RHS? 1 mark
3.3 Substitute x = 3 into the expression 2x + 1. What number do you get? 1 mark
3.4 Is x = 4 a solution of x + 8 = 12? Substitute and compare. 1 mark
Standard — combine ideas
3.5 Check whether x = 5 is a solution of 3x + 2 = 17. Show LHS, RHS and your conclusion. 2 marks
3.6 Check whether x = 5 is a solution of 3x − 4 = 10. If it is not, what value of x would work? 2 marks
Extension — push your thinking
3.7 Is x = 2 a solution of x² + 3 = 7? Show LHS, RHS, and explain in one sentence what x² means. 3 marks
3.8 A classmate says "the equation 6 = 6 is silly because there is no x." Is 6 = 6 a true equation? Is it useful? Write two sentences explaining your answer. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (2x − 5 = 7, test x = 6)
Step 1: LHS = 2x − 5, RHS = 7.
Step 2: LHS = 2(6) − 5 = 12 − 5 = 7.
Step 3: LHS = 7, RHS = 7 → LHS = RHS ✓.
Step 4: Therefore x = 6 is a solution.
3.1 — Expression or equation?
(a) 3x + 7 → expression (no =). (b) 3x + 7 = 19 → equation. (c) y² = 16 → equation (has =).
3.2 — LHS and RHS of 4x − 3 = 9
LHS = 4x − 3. RHS = 9. The equals sign is the divider; both sides go in completely.
3.3 — Substitute x = 3 into 2x + 1
2(3) + 1 = 6 + 1 = 7.
3.4 — Is x = 4 a solution of x + 8 = 12?
LHS = 4 + 8 = 12. RHS = 12. LHS = RHS ✓. Yes, x = 4 is the solution.
3.5 — Check x = 5 in 3x + 2 = 17
LHS = 3(5) + 2 = 15 + 2 = 17. RHS = 17. LHS = RHS ✓. Yes, x = 5 is a solution.
3.6 — Check x = 5 in 3x − 4 = 10
LHS = 3(5) − 4 = 15 − 4 = 11. RHS = 10. LHS ≠ RHS ✗. No, x = 5 is not a solution. We need LHS = 10, so 3x = 14 and the value that works is x = 14⁄3 (or about 4.67).
3.7 — Is x = 2 a solution of x² + 3 = 7?
x² means x × x, so 2² = 2 × 2 = 4. LHS = 4 + 3 = 7. RHS = 7. LHS = RHS ✓. Yes, x = 2 is a solution.
3.8 — Is 6 = 6 a valid equation?
Yes, 6 = 6 is a true equation — the equals sign just claims the two sides are equal, and 6 obviously equals 6. It does not need to contain a variable. It is not very useful on its own (there's nothing to solve), but identity equations like this are important when checking arithmetic and when proving that two algebraic expressions are equivalent.