Mathematics • Year 7 • Unit 2 • Lesson 13
Solving One-Step Equations (Multiply/Divide)
Build the basics: when x is multiplied by a coefficient, divide both sides; when x is divided, multiply both sides. Mind the sign rules.
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 6x = 42.
Step 1 — Identify the operation on x.
6x means 6 × x → x is being MULTIPLIED by 6
Reason: in 6x, the 6 is the coefficient — the number multiplying x. To get x alone, we need to undo the multiplication.
Step 2 — Apply the inverse: divide BOTH sides by 6.
6x ÷ 6 = 42 ÷ 6
Reason: division undoes multiplication. The same operation on both sides keeps the scales balanced.
Step 3 — Simplify each side.
x = 7
Reason: on the left, 6 ÷ 6 = 1, leaving 1 × x = x. On the right, 42 ÷ 6 = 7.
Step 4 — Check by substitution.
6 × 7 = 42 ✓ matches the RHS
Answer: x = 7.
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 x⁄5 = 8.
Step 1 — Operation on x:
x is being _______________ by 5. Inverse is ____________________.
Step 2 — Apply the inverse to BOTH sides:
____ × (x⁄5) = ____ × 8
Step 3 — Simplify:
x = ____
Step 4 — Check:
Substitute back: ____ ÷ 5 = ____ ✓ matches RHS
3. You do — independent practice
Show your working — at minimum the inverse step on BOTH sides 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 5x = 35. 1 mark
3.2 Solve x⁄4 = 7. 1 mark
3.3 Solve 3x = 27. Check your answer. 1 mark
3.4 Solve x⁄2 = 8. Check your answer. 1 mark
Standard — negative coefficients
3.5 Solve −3x = 24. (Watch the sign — positive ÷ negative = negative.) 2 marks
3.6 Solve 8x = −64. 2 marks
Extension — two negatives and a division with a negative
3.7 Solve x⁄(−5) = −3. (Negative × negative = positive.) 2 marks
3.8 Solve x⁄7 = −5. Show your method and check. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (x⁄5 = 8)
Step 1: x is being divided by 5; inverse is multiply by 5.
Step 2: 5 × (x⁄5) = 5 × 8.
Step 3: x = 40.
Step 4: Check: 40 ÷ 5 = 8 ✓ matches RHS.
3.1 — 5x = 35
Divide both sides by 5: x = 35 ÷ 5 = 7. Check: 5 × 7 = 35 ✓.
3.2 — x⁄4 = 7
Multiply both sides by 4: x = 7 × 4 = 28. Check: 28 ÷ 4 = 7 ✓.
3.3 — 3x = 27
Divide both sides by 3: x = 27 ÷ 3 = 9. Check: 3 × 9 = 27 ✓.
3.4 — x⁄2 = 8
Multiply both sides by 2: x = 8 × 2 = 16. Check: 16 ÷ 2 = 8 ✓.
3.5 — −3x = 24
Divide both sides by −3: x = 24 ÷ (−3) = −8. Check: −3 × (−8) = 24 ✓.
3.6 — 8x = −64
Divide both sides by 8: x = −64 ÷ 8 = −8. Check: 8 × (−8) = −64 ✓.
3.7 — x⁄(−5) = −3
Multiply both sides by −5: x = (−3) × (−5) = 15. Check: 15 ÷ (−5) = −3 ✓.
3.8 — x⁄7 = −5
Multiply both sides by 7: x = (−5) × 7 = −35. Check: −35 ÷ 7 = −5 ✓.