How do I solve an equation with x on both sides?

Subtract the smaller x term from both sides so x appears on one side only, for example subtract 2x from 5x + 12 = 2x + 39.

Why does a term change sign when it is moved across?

Moving a term is the same as adding or subtracting the same number on both sides, so its sign becomes the opposite.

How do I choose the unknown in a word problem?

Let the compared or smallest quantity be x and express the rest in terms of x, for example width x and length x + 5.

P5 Maths Simple Equations Paper 4: Error Review

2026-11-09

Tutor Prep Guide · P5 Maths

Ten original items, each with an answer and a one-line explanation.

Direct answers　Items 1-3 are basic, 4-6 intermediate and 7-9 challenge, with item 10 as the error review. Time yourself first, then check every answer and redo the wrong ones.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	20
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: P5 Maths Simple Equations and Word Problems
Level	P5

02　Questions (10 items)

FoundationSolve x + 18 = 45.
FoundationSolve 7x = 84.
FoundationSolve x/6 = 9.
IntermediateSolve 4x − 13 = 47.
IntermediateSolve 3(x + 6) = 45.
IntermediateSolve 5x + 12 = 2x + 39.
ChallengeA book costs x dollars. Ming buys 3 books, pays 100 dollars and gets 13 dollars change. Find the price of one book.
ChallengeA rectangle is 5 cm longer than it is wide and its perimeter is 46 cm. Find the width in cm.
ChallengeTwo brothers save 72 dollars in total. The elder saves 3 times as much as the younger. How much does the younger save?
Error redoError review: a pupil solves 4x + 9 = 2x + 21, moves 9 across without changing its sign and answers x = 15. What is the correct answer?

03　Answers and one-line notes

#	Answer	One-line note
1	x = 27	Subtract 18 from both sides to get x = 27.
2	x = 12	Divide both sides by 7 to get x = 12.
3	x = 54	Multiply both sides by 6 to get x = 54.
4	x = 15	Add 13 to get 4x = 60, then divide by 4, so x = 15.
5	x = 9	Divide both sides by 3 to get x + 6 = 15, so x = 9.
6	x = 9	Subtract 2x to get 3x + 12 = 39, then 3x = 27, so x = 9.
7	29 dollars	The three books cost 100 − 13 = 87 dollars, so x = 87 ÷ 3 = 29 dollars.
8	9 cm	Let the width be x and the length x + 5, so 2(2x + 5) = 46, giving x = 9 cm.
9	18 dollars	Let the younger save x, then x + 3x = 72, so x = 18 dollars.
10	x = 6	Subtract 2x to get 2x + 9 = 21, then 2x = 12, so x = 6. A term moved across the equals sign must change sign.

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.

Book a Maths tutor Tutor Registration →

Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.