How do I handle the unknown on both sides?

Move all x terms to one side and the numbers to the other, for example subtract 3x from 3x + 7 = 5x − 9.

How do I solve an equation with fraction coefficients?

Multiply through by the denominators, for example rewrite x/3 + x/6 with the common denominator 6.

Any tip for choosing the unknown in a word problem?

Usually let the smallest or compared quantity be x and express the rest with x, for example width x and length x + 4.

P5 Maths Simple Equations Paper 3: Challenge

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 the equation 3x + 7 = 5x − 9.
FoundationSolve the equation 8(x − 3) = 5x + 6.
FoundationSolve the equation (x + 5) ÷ 3 = 7.
IntermediateSolve the equation 2(3x − 1) = 4x + 12.
IntermediateSolve the equation 0.5x + 3 = 9.
IntermediateSolve the equation x ÷ 3 + x ÷ 6 = 9.
ChallengeTwo numbers add up to 48 and the larger is 3 times the smaller. What is the smaller number?
ChallengeAn elder brother saves x dollars and his younger brother saves 15 dollars less. Together they save 85 dollars. How much does the elder brother save?
ChallengeA rectangle is 4 cm longer than it is wide and its perimeter is 36 cm. Find the width in cm.
Error redoError review: a pupil solves 5x − 3 = 2x + 12 and answers x = 3. What is the correct answer?

03　Answers and one-line notes

#	Answer	One-line note
1	x = 8	Subtract 3x to get 7 = 2x − 9, then add 9 to get 16 = 2x, so x = 8.
2	x = 10	Expand to get 8x − 24 = 5x + 6, so 3x = 30 and x = 10.
3	x = 16	Multiply both sides by 3 to get x + 5 = 21, so x = 16.
4	x = 7	Expand to get 6x − 2 = 4x + 12, so 2x = 14 and x = 7.
5	x = 12	Subtract 3 to get 0.5x = 6, then multiply by 2 to get x = 12.
6	x = 18	With a common denominator, 2x/6 + x/6 = 3x/6 = 9, so 3x = 54 and x = 18.
7	12	Let the smaller be x, then x + 3x = 48, so 4x = 48 and x = 12.
8	50 dollars	The younger brother saves x − 15, so x + (x − 15) = 85, giving 2x = 100 and x = 50.
9	7 cm	Let the width be x, so the length is x + 4 and 2(2x + 4) = 36, giving x = 7.
10	x = 5	Subtract 2x to get 3x − 3 = 12, then add 3 to get 3x = 15, so x = 5. The pupil divided wrongly.

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.