Equations with Brackets and Unknowns on Both Sides - Worksheets, Questions and Revision

30 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 7)Equations with Brackets and Unknowns on Both Sides revision guide

This topic is chapter 8 of KS3 Maths: Algebra Practice Book 1.

Next in this strand

2.11 Equations with Brackets and Unknowns on Both Sides

AQA KS3.M-A11 · Calculators not allowed · about 90 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Solve -2(x - 4) = 10

(3)

Solve 2(x + 3) = 3(x - 1) + 1

(3)

Solve 2(x + 4) - 3 = x + 9

(3)

Solve 3(x - 2) = 2(x + 4) + 1

(3)

Kwame is 3 less than twice Erin. Their ages add to 33. Write equations to represent this and find their ages.

(4)

Solve 3(x - 2) = 9

(2)

Solve 4x + 5 = 21

(2)

Solve 5(x + 1) = 3x + 11

(3)

Solve 2(x - 4) + 3 = 7

(3)

Solve 3(x + 2) = 2x + 9

(2)

Priya has x boxes of postcards. Each box contains 4 postcards and she also has 5 loose postcards. Altogether she has 29 postcards. Form an equation and solve it for x.

(3)

Solve x/2 + 3 = 11

(2)

Solve 2(2x - 3) = 3x + 1

(3)

Solve 3(x + 2) = 18.

(1)

Solve (2/3)x + 1 = 9.

(2)

Solve 2(x + 5) - 4 = x + 10.

(2)

Solve 4(x + 3) = 28.

(1)

Solve 5(x - 2) = 15.

(1)

Solve 4(x - 3) = 3(x + 1) + 2.

(2)

Aisha is 4 years older than twice Ben's age. Their ages add to 34. Write an equation using b for Ben's age and find both of their ages.

(3)

Solve 3(2x - 1) = 5(x + 1). State the value of x.

(3)

Five equal boxes each contain x stickers, and there are 9 extra stickers. Altogether there are 79 stickers. Form an equation and solve it for x. Show your check.

(4)

Solve 4(x - 1) = 16.

(1)

Solve 2(x + 5) = 3x + 4.

(2)

Solve 3(x - 1) + 5 = 11.

(2)

Solve 5(x + 2) = 2x + 20.

(2)

Solve x/3 + 4 = 9.

(2)

Solve 2(3x - 2) = 4x + 6.

(2)

Solve -3(x - 2) = 15.

(2)

Solve 3(x + 4) = 4(x - 2) + 6.

(2)

Mark scheme · 2.11 Equations with Brackets and Unknowns on Both Sides

Question 1

M1 expand the bracket: -2x + 8 = 10
M1 rearrange and divide: -2x = 2 so x = -1
A1 x = -1 cao
Answer: -1

Question 2

M1 expand both brackets and simplify: 2x + 6 = 3x - 3 + 1
M1 collect like terms: 2x + 6 = 3x - 2 so x = 8
A1 x = 8 cao
Answer: 8

Question 3

M1 expand and simplify left side: 2x + 8 - 3 = x + 9 giving 2x + 5 = x + 9
M1 collect x terms then subtract: x = 4
A1 x = 4 cao
Answer: 4

Question 4

M1 expand both sides: 3x - 6 = 2x + 8 + 1
M1 collect like terms to isolate x: x = 15
A1 x = 15 cao
Answer: 15

Question 5

M1 correct first equation: K = 2E - 3 or equivalent
M1 correct sum equation substituting K: (2E - 3) + E = 33 or 3E - 3 = 33
A1 E = 12 cao
A1 K = 21 cao
Answer: Erin = 12, Kwame = 21

Question 6

M1 divide both sides by 3 or expand then divide: x - 2 = 3 or 3x - 6 = 9
A1 x = 5 cao
Answer: 5

Question 7

M1 subtract 5 then divide by 4: 4x = 16
A1 x = 4 cao
Answer: 4

Question 8

M1 expand the bracket: 5x + 5 = 3x + 11
M1 collect like terms to isolate x: 2x = 6
A1 x = 3 cao
Answer: 3

Question 9

M1 expand and simplify: 2x - 8 + 3 = 7 giving 2x - 5 = 7
M1 add 5 then divide by 2: 2x = 12
A1 x = 6 cao
Answer: 6

Question 10

M1 expand the bracket or rearrange: 3x + 6 = 2x + 9
A1 x = 3 cao
Answer: 3

Question 11

M1 correct formation: 4x + 5 = 29 or equivalent equation
M1 subtract 5 then divide by 4 to find x
A1 x = 6 cao
Answer: 6

Question 12

M1 subtract 3 then multiply by 2: x/2 = 8
A1 x = 16 cao
Answer: 16

Question 13

M1 expand left side: 4x - 6 = 3x + 1
M1 collect x terms: x = 7
A1 x = 7 cao
Answer: 7

Question 14

B1 x = 4 cao
Answer: x = 4

Question 15

M1 correct first step, e.g. (2/3)x = 8
A1 x = 12 cao
Answer: x = 12

Question 16

M1 expands bracket: 2x + 10 - 4 = x + 10
A1 x = 4 cao
Answer: x = 4

Question 17

B1 x = 4 cao
Answer: x = 4

Question 18

B1 x = 5 cao
Answer: x = 5

Question 19

M1 expands both brackets: 4x - 12 = 3x + 3 + 2
A1 x = 17 cao
Answer: x = 17

Question 20

M1 forms b + (2b + 4) = 34
M1 correct rearrangement, e.g. 3b = 30
A1 Ben = 10, Aisha = 24
Answer: Ben = 10, Aisha = 24

Question 21

M1 expands both brackets: 6x - 3 = 5x + 5
M1 correct rearrangement, e.g. x = 8
A1 x = 8 cao
Answer: x = 8

Question 22

M1 forms 5x + 9 = 79
M1 correct rearrangement, e.g. 5x = 70
A1 x = 14 cao
B1 check shown: 5(14) + 9 = 79
Answer: x = 14

Question 23

B1 x = 5 cao
Answer: x = 5

Question 24

M1 expands bracket: 2x + 10 = 3x + 4
A1 x = 6 cao
Answer: x = 6

Question 25

M1 expands bracket: 3x - 3 + 5 = 11
A1 x = 3 cao
Answer: x = 3

Question 26

M1 expands bracket: 5x + 10 = 2x + 20
A1 x = 10/3 cao
Answer: x = 10/3

Question 27

M1 correct first step, e.g. x/3 = 5
A1 x = 15 cao
Answer: x = 15

Question 28

M1 expands bracket: 6x - 4 = 4x + 6
A1 x = 5 cao
Answer: x = 5

Question 29

M1 expands bracket correctly: -3x + 6 = 15
A1 x = -3 cao
Answer: x = -3

Question 30

M1 expands both brackets: 3x + 12 = 4x - 8 + 6
A1 x = 14 cao
Answer: x = 14

Equations with Brackets and Unknowns on Both Sides - Worksheets, Questions and Revision

Next in this strand

Related topics

2.11 Equations with Brackets and Unknowns on Both Sides

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

Question 28

Question 29

Question 30

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

Question 28

Question 29

Question 30