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 ✓.