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© John Wiley & Sons Australia, Ltd Page 1
WorkSHEET 2.2 Solving equations with fractions Name: ___________________________ 1 Solve the following equations:
(a) 7m – 3 = 39 (b) 6n + 4 = −8
(a) 7m - 3 = 39 7m - 3 + 3 = 39 + 3 7m = 42
742
77
=m
m = 6
(b) 6n + 4 = −8 6n + 4 - 4 = −8 - 4 6n = −12
6 126 6n -=
n = −2 2 Solve the following equations:
(a) 13 95g- = -
(b) 2123114
=+h
(a) 13 95
13 13 9 135
45
5 4 55
20
g
g
g
g
g
- = -
- + = - +
=
´ = ´
=
4(b) 23 2111
4 23 23 21 2311
4 211
4 11 2 1111
4 224 224 4
152
h
h
h
h
hh
h
+ =
+ - = -
= -
´ = - ´
= --
=
= -
© John Wiley & Sons Australia, Ltd Page 2
3 Solve the following equations: (a) 4(3 5) 4f + = -
50)92(6)b( =-s
(a) 4(3 5) 4
12 20 412 20 20 4 20
12 2412 2412 12
2
ff
fff
f
+ = -+ = -
+ - = - -= --
=
= -
or
4(3 5) 44(3 5) 4
4 43 5 1
3 5 5 1 53 63 63 3
2
ff
ff
ff
f
+ = -+ -
=
+ = -+ - = - -
= --
=
= -
328
32612104
1212
104125450545412
50541250)92(6)b(
=
=
=
=+=+-
=-=-
s
s
ss
sss
© John Wiley & Sons Australia, Ltd Page 3
4 Solve the following equations: (a) 14 4 6t- = -
9733)b( =-u
(a) 14 4 64 14 6
4 14 14 6 144 204 204 4
5
tt
ttt
t
- = -- + = -
- + - = - -- = -- -
=- -
=
3(b) 3 97
3 3 97
3 3 3 9 37
3 67
3 7 6 773 423 423 3
14
u
u
u
u
u
uu
u
- =
-+ =
-+ - = -
-=
-´ = ´
- =-
=- -
= -
5 Solve the following equations: (a) 3y – 7 = 7 + y (b) 16z - 11 = 20z - 3
(a) 3y – 7 = 7 + y 3y - y - 7 = 7 + y - y 2y – 7 = 7 2y - 7 + 7 = 7 + 7 2y = 14
214
22
=y
y = 7 (b) 16z - 11 = 20z - 3 16z - 11 - 16z = 20z - 3 - 16z −11 = 4z - 3 4z - 3 = −11 4z - 3 + 3 = −11 + 3 4z = −8
4 84 4z -=
z = −2
© John Wiley & Sons Australia, Ltd Page 4
6 Solve the following equations: (a) 4(2c – 5) = 7(3c – 1) (b) −(3 – d) = 4(2d + 8)
(a) 4(2c – 5) = 7(3c – 1)
8c – 20 = 21c – 7 8c - 20 - 8c = 21c - 7 - 8c −20 = 13c - 7 13c - 7 = −20 13c - 7 + 7 = −20 + 7 13c = −13
13 1313 13c -=
c = −1 (b) −(3 – d) = 4(2d + 8)
−3 + d = 8d + 32 −3 + d - d = 8d + 32 - d −3 = 7d + 32 7d + 32 = −3 7d + 32 - 32 = −3 - 32 7d = −35
7 357 7d -=
d = −5
© John Wiley & Sons Australia, Ltd Page 5
7 Solve the following equations: (a) 6(2f – 1) + 3(4 – 2f) = 2(f + 1) + 2(f + 6) (b) 2(4 – g) – 3(2g – 6) = 8(3g – 1) – 11(g – 5)
(a) 6(2f – 1) + 3(4 – 2f) = 2(f + 1) + 2(f + 6) 12f – 6 + 12 – 6f = 2f + 2 + 2f + 12 6f + 6 = 4f + 14 6f + 6 - 4f = 4f + 14 - 4f 2f + 6 = 14 2f + 6 - 6 = 14 - 6 2f = 8
28
22
=f
f = 4 (b) 2(4 – g) – 3(2g – 6) = 8(3g – 1) – 11(g – 5)
8 – 2g – 6g + 18 = 24g – 8 – 11g + 55 26 – 8g = 13g + 47 26 - 8g + 8g = 13g + 47 + 8g 26 = 21g + 47 21g + 47 = 26 21g + 47 - 47 = 26 - 47 21g = −21
21 2121 21g -=
g = −1
8 Solve the following equations.
(a) 3 24 2 5x x+ =
(b) 2 4 35 3 4x x-- =
(a) 3 24 2 5x x+ =
5 30 820 20 20
35 820 2035 8
835
x x
x
x
x
+ =
=
=
=
(b) 2 4 35 3 4x x-- =
24 80 4560 60 60
104 4560 60104 45
45104
x x
x
x
x
-- =
-=
- =
= -
© John Wiley & Sons Australia, Ltd Page 6
9 Solve the following equations.
(a) 4 432 5x x- +
= +
(b) 2( 3) 3( 4)15 2x x+ -
- =
(a) 4 432 5x x- +
= +
5( 4) 30 2( 4)10 10 10
5( 4) 30 2( 4)5 20 30 2 85 2 30 8 20
3 585831193
x x
x xx xx x
x
x
x
- += +
- = + +- = + +- = + +
=
=
=
(b) 2( 3) 3( 4)15 2x x+ -
- =
4( 3) 10 15( 4)10 10 104( 3) 10 15( 4)4 12 10 15 604 15 60 12 10
11 6262117511
x x
x xx xx x
x
x
x
+ -- =
+ - = -+ - = -
- = - - +- = -
-=-
=
10 If 𝑢 = 𝑥 + 3 and 𝑣 = 𝑥 − 4, solve for 𝑥 where;
2𝑢5 − 1 =
3𝑣2
By sub we have;
2(𝑥 + 3)5 − 1 =
3(𝑥 − 4)2
Now just refer to previous solution to question 9 (b).
© John Wiley & Sons Australia, Ltd Page 7
11 Solve the following equations.
(a) 5 31 2x x=
- +
(b) 4 23( 6) 5( 4)x x
=+ -
(a) 5 31 2x x=
- +
5( 2) 3( 1)( 1)( 2) ( 1)( 2)
5( 2) 3( 1)5 10 3 35 3 3 10
2 13132162
x xx x x x
x xx xx x
x
x
x
+ -=
- + - ++ = -+ = -- = - -
= --
=
= -
(b) 4 23( 6) 5( 4)x x
=+ -
20( 4) 6( 6)15( 6)( 4) 15( 6)( 4)
20( 4) 6( 6)20 80 6 3620 6 36 80
14 11611614287
x xx x x x
x xx xx x
x
x
x
- +=
+ - + -- = +- = +- = +
=
=
=
