worksheet 11.2 linear equations...

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WorkSHEET 11.2 Linear equations Name: ___________________________ 1 Solve the following equations.

(a) m + 14

= 34

(b) 6l = -3.8

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

Answers:

(a) m + 14

= 34

m + 1 1 3 14 4 4 4- = -

m = 24

= 12

(b) 6l = -3.8

6l ´ 6 = -3.8 ´ 6

l = -22.8

(c) 2x + 4 = 5

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

2 12 2x=

x = 12

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

4( 10) 124 4y- +

=- -

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

WorkSHEET 11.2 Linear equations


2 Solve the following equations.

(a) 32e + = 4

(b) 67f- = 2

Answers:

(a) 3 42e+

=

( 3) 2 4 22e+

´ = ´

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

(b) 67f- = 2

67f- ´ 7 = 2 ´ 7

-6f = 14

6 146 6f-=

- -

f = -146

= - 7 1or 23 3

-

3 Are the following statements true or false?

(a) x = 6 is the solution to 2 17x + = 4 3

5x - .

(b) x = -1 is the solution to x2 = 2 + x.

Answers:

(a) LHS = 2 17x + RHS = 4 3

5x -

LHS = 2 6 17

´ + RHS = 4 6 35

´ -

LHS = 137

RHS = 215

False, since LHS ¹ RHS

(b) LHS = x2 RHS = 2 + x LHS = (-1)2 RHS = 2 + -1 LHS = 1 RHS = 2 - 1 RHS = 1 True, since LHS = RHS



4 Solve the following equations.

(a) 2 53d+ =

(b) 67 109g

- =

Answers:

(a) 2 53d+ =

2 2 5 23d+ - = -

3d = 3

3d ´ 3 = 3 ´ 3

d = 9

(b) 67 109g

- =

6 7 109g

- + =

6 7 7 109g

- + - = - 7

6 39

6 9 3 996 276 276 6

2769 1or 42 2

g

g

gg

g

g

- =

-´ = ´

- =-

=- -

=-

= - -



5 Solve the equations below.

(a) 5 23x- = 9

(b) 2( 2)4y - +7 = 14

Answers:

(a) 5 23x- = 9

(5 2 ) 33x-´ = 9 ´ 3

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

2 222 2x-=

- -

x = -11

(b) 2( 2)4y - + 7 = 14

2( 2)4y - + 7 - 7 = 14 - 7

2( 2)4y - = 7

2( 2)4y - ´ 4 = 7 ´ 4

2(y - 2) = 28

2( 2) 282 2y -

=

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

6 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

5 155 5d -=

d = -3

(b) 18 - 4e = e + 3 18 - 4e + 4e = e + 3 + 4e 18 = 5e + 3 5e + 3 = 18 5e + 3 - 3 = 18 - 3 5e = 15

5 155 5e=

e = 3



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 3 2 104 8

2

w www

+ = -==

b 10 21 3 2

12 242

z zzz

+ = - -= -= -

c 3 4 25 711 22

2

q qqq

+ = -==

d

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

+ - = + ++ - = + +

- = +==

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

6 66 6v=

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

7 147 7w=

w = 2



9 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.

2 4 663 6 66

3 6 6 66 63 603 603 3

20

x x xx

xxx

x

+ + + + =+ =

+ - = -=

=

= The numbers are 20, 22 and 24.

10

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

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

+ = -+ = -

+ + = - ++ =

+ - = -

=

==

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



11 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: 120 135 142

3255 1423

(255 ) 3 142 33

x

x

x

+ +=

+=

+´ = ´

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

12 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.

6 3222 6 3222 316

158 cm

x xxxx

+ + =+ =

==

Penny is 158 cm tall.

worksheet 11.2 linear equations...

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