© John Wiley & Sons Australia, Ltd 1

Year 8 11.2 Linear equations Name: ___________________________ 1 Solve the following equations.

(a) m + =

(b) = -3.8

(c) 2x + 4 = 5 (d) - 4(y + 10) = 12

Answers:

(a) m + =

m +

m =

=

(b) = -3.8

´ 6 = -3.8 ´ 6

l = -22.8

(c) 2x + 4 = 5

2x + 4 - 4 = 5 - 4 2x = 1

x =

(d) - 4(y + 10) = 12

y + 10 = -3 y + 10 - 10 = -3 - 10 y = -13

14

34

6l

14

34

1 1 3 14 4 4 4- = -

2412

6l

6l

2 12 2x=

12

4( 10) 124 4y- +

=- -

WorkSHEET 11.2 Linear equations

© John Wiley & Sons Australia, Ltd 2

2 Solve the following equations.

(a) = 4

(b) = 2

Answers:

(a)

e + 3 = 8 e + 3 - 3 = 8 - 3 e = 5

(b) = 2

´ 7 = 2 ´ 7

-6f = 14

f = -

= -

3 Solve the following equations. (a) 3d + 4 = -11 - 2d (b) 18 - 4e = e + 3

Answers: (a) 3d + 4 = -11 - 2d

3d + 4 + 2d = -11 - 2d + 2d 5d + 4 = -11 5d + 4 - 4 = -11 - 4 5d = -15

d = -3

18 - 4e = e + 3 18 - 4e + 4e = e + 3 + 4e 18 = 5e + 3 5e + 3 = 18 5e + 3 - 3 = 18 - 3 5e = 15

e = 3

32e +

67f-

3 42e+

=

( 3) 2 4 22e+

´ = ´

67f-

67f-

6 146 6f-=

- -1467 1or 23 3

-

5 155 5d -=

5 155 5e=

WorkSHEET 11.2 Linear equations

© John Wiley & Sons Australia, Ltd 3

4 Solve the following equations.

(a)

(b)

Answers:

(a)

= 3

´ 3 = 3 ´ 3

d = 9

(b)

- 7

5 Joshua is 6 cm taller than Penny. If their total height is 322 cm, how tall is Penny?

Answer: Let x be Penny’s height.

Penny is 158 cm tall.

2 53d+ =

67 109g

- =

2 53d+ =

2 2 5 23d+ - = -

3d

3d

67 109g

- =

6 7 109g

- + =

6 7 7 109g

- + - =

6 39

6 9 3 996 276 276 6

2769 1or 42 2

g

g

gg

g

g

- =

-´ = ´

- =-

=- -

=-

= - -

6 3222 6 3222 316

158 cm

x xxxx

+ + =+ =

==

WorkSHEET 11.2 Linear equations

© John Wiley & Sons Australia, Ltd 4

6 Solve the equations below.

(a) = 9

(b) +7 = 14

Answers:

(a) = 9

= 9 ´ 3

5 - 2x = 27 -2x + 5 = 27 -2x + 5 - 5 = 27 - 5 -2x = 22

x = -11

(b) + 7 = 14

+ 7 - 7 = 14 - 7

= 7

´ 4 = 7 ´ 4

2(y - 2) = 28

y - 2 = 14 y - 2 + 2 = 14 + 2 y = 16

7 Solve the following equations. a 3w + 2 = 10 - w b 10z + 21 = -3 - 2z c 3 + 4q = 25 - 7q d 6r + 2(4r - 3) = 6 + 5(r + 3)

Answers:

a

b

c

d

5 23x-

2( 2)4y -

5 23x-

(5 2 ) 33x-´

2 222 2x-=

- -

2( 2)4y -

2( 2)4y -

2( 2)4y -

2( 2)4y -

2( 2) 282 2y -

=

3 2 104 8

2

w www

+ = -==

10 21 3 212 24

2

z zzz

+ = - -= -= -

3 4 25 711 22

2

q qqq

+ = -==

6 2(4 3) 6 5( 3)6 8 6 6 5 1514 6 5 21

9 273

r r rr r r

r rrr

+ - = + ++ - = + +

- = +==

WorkSHEET 11.2 Linear equations

© John Wiley & Sons Australia, Ltd 5

8 Expand the brackets first and then solve the equation. (a) 4(2 - v) = 2v + 2 (b) w + 4 = 2(4w - 5)

Answers:

(a) 4(2 - v) = 2v + 2 8 - 4v = 2v + 2 8 - 4v + 4v = 2v + 2 + 4v 8 = 6v + 2 6v + 2 = 8 6v + 2 - 2 = 8 - 2 6v = 6

v = 1

(b) w + 4 = 2(4w - 5) w + 4 = 8w - 10 w - w + 4 = 8w - 10 - w 4 = 7w - 10 7w - 10 = 4 7w - 10 + 10 = 4 + 10 7w = 14

w = 2

9 Three consecutive numbers add up to 18. What are the numbers?

Answers: Let x be the first number, x + 1 the second and x + 2 the third.

𝑥 + 𝑥 + 1 + 𝑥 + 2 = 18

3𝑥 + 3 = 18

3𝑥 = 15

𝑥 = 5 The numbers are 5, 6 and 7.

6 66 6v=

7 147 7w=

WorkSHEET 11.2 Linear equations

© John Wiley & Sons Australia, Ltd 6

10 Three consecutive even numbers add up to 66. What are the numbers?

Answers: Let x be the first number, x + 2 the second and x + 4 the third.

The numbers are 20, 22 and 24.

11 Make up one of these yourself, and then check it. Eg. Four consecutive numbers add 14. What are the numbers?

12

These two rectangles have the same area. Write an equation and solve it to find x. What is the area of each rectangle? (All lengths are in metres.)

Answers: Recall A = l ´ w

Substitute x = 4 into either area formula. Area = l ´ w Area = (x + 2) ´ 12 Area = (4 + 2) ´ 12 Area = 6 ´ 12 Area = 72 m2 or Area = l ´ w Area = (13 - x) ´ 8 Area = (13 - 4) ´ 8 Area = 9 ´ 8 Area = 72 m2

2 4 663 6 66

3 6 6 66 63 603 603 3

20

x x xx

xxx

x

+ + + + =+ =

+ - = -=

=

=

12( 2) 8(13 )12 24 104 8

12 24 8 104 8 820 24 104

20 24 24 104 2420 8020 2020 80

4

x xx x

x x x xx

xx

xx

+ = -+ = -

+ + = - ++ =

+ - = -

=

==

WorkSHEET 11.2 Linear equations

© John Wiley & Sons Australia, Ltd 7

13 At tenpin bowling, Amanda bowled games of 120 and 135. How much must she score in her next game to attain an average of 142?

Answer:

255 + x = 426 255 - 255 + x = 426 - 255 x = 171 Amanda must score 171 in her next game to attain an average of 142.

14 If you want a “WB”, is doing this worksheet enough?

NO. I need to do worksheets twice as well as doing ALL the term planner questions twice also!

120 135 1423255 1423

(255 ) 3 142 33

x

x

x

+ +=

+=

+´ = ´