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KS3 · Algebra

KS3.M-A11 Equations with Brackets and Unknowns on Both Sides

AQA KS3.M-A11 · Calculators not allowed · about 60 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Solve 2(x + 3) = 14

(2)

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 -2(x - 4) = 10

(3)

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

(3)

Five boxes each contain (x + 2) stickers. Altogether there are 65 stickers. Form an equation and solve for x.

(3)

Solve (3/4)x + 2 = 11

(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 4(x + 1) - (x - 2) = 2x + 9

(3)

Solve 2(x + 3) = 2x + 6. State whether there is a unique solution, no solution or infinitely many solutions and explain briefly.

(3)

Mark scheme · KS3.M-A11 Equations with Brackets and Unknowns on Both Sides

Question 1

M1 expand the bracket or divide both sides by 2 after simplifying: 2x + 6 = 14 or x + 3 = 7
A1 x = 4 cao
Answer: 4

Question 2

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

Question 3

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

Question 4

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

Question 5

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 6

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

Question 7

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 8

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

Question 9

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

Question 10

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

Question 11

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 12

M1 correct formation: 5(x + 2) = 65
M1 expand or divide then solve: x + 2 = 13 or 5x + 10 = 65
A1 x = 11 cao
Answer: 11

Question 13

M1 subtract 2 then multiply by 4/3: (3/4)x = 9
M1 x = 9 * (4/3) or x = 12
A1 x = 12 cao
Answer: 12

Question 14

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 15

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 16

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 17

M1 expand and remove brackets: 4x + 4 - x + 2 = 2x + 9 giving 3x + 6 = 2x + 9
M1 collect x terms to give x = 3
A1 x = 3 cao
Answer: 3

Question 18

M1 expand both sides or simplify to show 2x + 6 = 2x + 6
M1 recognise that the variable terms cancel giving a true statement 6 = 6
A1 infinitely many solutions cao (any x satisfies the equation)
Answer: Infinitely many solutions

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