Mathematics • Year 7 • Unit 2 • Lesson 14
Two-Step Equations
Build the basics: undo two operations in REVERSE order (SADMEP — Subtract/Add first, then Divide/Multiply) to isolate x.
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. Solve 5x − 3 = 22.
Step 1 — Identify what's being done to x, in order.
First: × 5 (because 5x means 5 × x). Then: − 3.
Reason: BEDMAS — multiplication happens before subtraction. To UNDO, reverse the order: undo the −3 first, then the ×5. This is SADMEP.
Step 2 — Undo the −3 first (add 3 to BOTH sides).
5x − 3 + 3 = 22 + 3 → 5x = 25
Reason: addition undoes subtraction. The +3 cancels the −3 on the left, leaving just 5x. On the right, 22 + 3 = 25.
Step 3 — Undo the ×5 (divide BOTH sides by 5).
5x ÷ 5 = 25 ÷ 5 → x = 5
Reason: division undoes multiplication. The ÷5 cancels the ×5 on the left, leaving just x.
Step 4 — Check by substitution.
5(5) − 3 = 25 − 3 = 22 ✓ matches the RHS
Answer: x = 5.
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. Solve 3x + 4 = 19.
Step 1 — Operations on x, in order:
First: × ____ , then: + ____ . To undo, reverse: ____________ first, then ____________ .
Step 2 — Undo the +4 first (subtract 4 from BOTH sides):
3x + 4 − ____ = 19 − ____ → 3x = ____
Step 3 — Undo the ×3 (divide BOTH sides by 3):
3x ÷ ____ = ____ ÷ 3 → x = ____
Step 4 — Check:
Substitute: 3(____) + 4 = ____ + 4 = ____ ✓ matches RHS
3. You do — independent practice
Show your working — at minimum BOTH inverse steps and the final answer. The first four are foundation, the middle two are standard, and the last two are extension.
Foundation — clean whole numbers
3.1 Solve 2x + 5 = 17. 1 mark
3.2 Solve 4x − 7 = 5. 1 mark
3.3 Solve 6x − 1 = 23. Check your answer. 1 mark
3.4 What is the FIRST step to solve 5x − 8 = 27? (Don't solve yet — just name the move and write the equation after that move.) 1 mark
Standard — division equations and decimals
3.5 Solve x⁄6 − 3 = 4. (Hint: undo the −3 first, then undo the ÷6.) 2 marks
3.6 Solve 4x + 2.5 = 18.5. 2 marks
Extension — negatives and a fraction answer
3.7 Solve −3x + 11 = 2. (The coefficient is negative.) 2 marks
3.8 Solve 2x + 7 = 12. (Answer is a fraction or decimal.) 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (3x + 4 = 19)
Step 1: × 3 then + 4. To undo, reverse: subtract 4 first, then divide by 3.
Step 2: 3x + 4 − 4 = 19 − 4 → 3x = 15.
Step 3: 3x ÷ 3 = 15 ÷ 3 → x = 5.
Step 4: 3(5) + 4 = 15 + 4 = 19 ✓ matches RHS.
3.1 — 2x + 5 = 17
Subtract 5: 2x = 12. Divide by 2: x = 6. Check: 2(6) + 5 = 17 ✓.
3.2 — 4x − 7 = 5
Add 7: 4x = 12. Divide by 4: x = 3. Check: 4(3) − 7 = 5 ✓.
3.3 — 6x − 1 = 23
Add 1: 6x = 24. Divide by 6: x = 4. Check: 6(4) − 1 = 23 ✓.
3.4 — First step for 5x − 8 = 27
Add 8 to BOTH sides. New equation: 5x = 35. (We'd then divide by 5 to get x = 7.)
3.5 — x⁄6 − 3 = 4
Add 3 to both sides: x⁄6 = 7. Multiply both sides by 6: x = 42. Check: 42⁄6 − 3 = 7 − 3 = 4 ✓.
3.6 — 4x + 2.5 = 18.5
Subtract 2.5: 4x = 16. Divide by 4: x = 4. Check: 4(4) + 2.5 = 16 + 2.5 = 18.5 ✓.
3.7 — −3x + 11 = 2
Subtract 11: −3x = −9. Divide by −3: x = 3 (negative ÷ negative = positive). Check: −3(3) + 11 = −9 + 11 = 2 ✓.
3.8 — 2x + 7 = 12
Subtract 7: 2x = 5. Divide by 2: x = 2.5 (or 5⁄2). Check: 2(2.5) + 7 = 5 + 7 = 12 ✓.