In 28 − x = 11, why can I just write x = 28 − 11?

Adding x to both sides gives 28 = 11 + x, which leads to the same 17. In a subtraction the part taken away plus the difference makes the whole, so 28 − 11 is the shortest route, as long as the reason can be stated.

In 56 − 4x = 24 the right step is 4x = 56 − 24. Why not 4x = 56 + 24?

The minus in front of 4x means it is taken out of 56, leaving 24. So the part taken away is the gap between 56 and 24: 4x = 56 − 24 = 32. Writing 56 + 24 treats that part as something added, which makes the answer too large.

Primary 5 Maths: Simple Equations — Practice Paper 4 (10 Questions)

2026-10-29

Tutor Prep Guide · Primary Maths

Paper 4 completes the set of four: equations where x is the part taken away (28 − x = 11, 56 − 4x = 24), plus 7x − 19 = 44, a change problem and “six times minus nine”. Check every answer by substitution.

Quick answer　10 questions, about 25 minutes. Items 01 to 04 are one-step equations, items 05 and 06 are two-step equations, item 07 puts x on the subtracted side, items 08 and 09 form equations from words, item 10 targets the direction error of adding instead of subtracting.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	25 minutes
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: Primary 5 Maths: Simple Equations — Tutor Lesson Plan
Level	Primary 5

02　Questions (10 items)

FoundationSolve: x + 34 = 71
FoundationSolve: x − 26 = 45
FoundationSolve: 9x = 117
FoundationSolve: x ÷ 8 = 12
IntermediateSolve: 3x + 16 = 49
IntermediateSolve: 7x − 19 = 44
IntermediateSolve: 28 − x = 11 (x is the part being taken away)
ChallengeWah takes $x to buy 5 pens at $6 each and has $18 left. Write “let x be …”, then an equation, and find x.
ChallengeSix times a number minus 9 equals 63. Let the number be x, form an equation and find x.
Error redoSolve: 56 − 4x = 24 (common slip: adding instead of subtracting and getting x = 20)

03　Answers and one-line notes

#	Answer	One-line note
1	x = 37	Subtract 34 from both sides: x = 71 − 34 = 37, and 37 + 34 = 71 checks it.
2	x = 71	Add 26 to both sides: x = 45 + 26 = 71, and 71 − 26 = 45 checks it.
3	x = 13	9x is nine x, so divide both sides by 9: x = 117 ÷ 9 = 13, and 9 × 13 = 117.
4	x = 96	x is divided by 8, so multiply both sides by 8: x = 12 × 8 = 96, and 96 ÷ 8 = 12.
5	x = 11	Subtract 16 for 3x = 33, then divide by 3 for x = 11; 3 × 11 + 16 = 49.
6	x = 9	Add 19 for 7x = 63, then divide by 7 for x = 9; 7 × 9 − 19 = 44.
7	x = 17	28 minus x leaves 11, so x is the gap between them: x = 28 − 11 = 17, and 28 − 17 = 11.
8	5 pens cost $30, so x − 30 = 18 and x = 48	Five pens cost 5 × 6 = $30; taking that from the money gives 18: x − 30 = 18, so x = 48.
9	6x − 9 = 63, so x = 12	“Six times minus 9” becomes 6x − 9: add 9 for 6x = 72, divide by 6 for x = 12; 6 × 12 − 9 = 63.
10	x = 8	4x is the part being taken away, so 4x = 56 − 24 = 32 and x = 8; 56 − 4 × 8 = 24.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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